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Most viewed questions in Probability and Statistics
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41
TIFR ECE 2018 | Question: 9
Let $X$ and $Y$ be two independent and identically distributed binary random variables that take values $\{-1,+1\}$ each with probability $1 / 2$. Let $Z_{1}=\max (X, Y)$, and $Z_{2}=\min (X, Y)$. Consider the following statements. $Z_{1}$ and $Z_{2}$ are uncorrelated ... $\text{(iii)}$ Both $\text{(i) and (ii), but not (iii)}$ All of $\text{(i), (ii) and (iii)}$
Let $X$ and $Y$ be two independent and identically distributed binary random variables that take values $\{-1,+1\}$ each with probability $1 / 2$. Let $Z_{1}=\max (X, Y)$...
admin
46.4k
points
117
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admin
asked
Nov 29, 2022
Probability and Statistics
tifrece2018
probability-and-statistics
probability
random-variable
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0
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0
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42
GATE ECE 2017 Set 2 | Question: 22
Consider the random process $X(t)=U+Vt,$ Where $U$ is a zero-mean Gaussian random variable and V is a random variable uniformly distributed between $0$ and $2$. Assume that $U$ and $V$ are statistically independent. The mean value of the random process at $t = 2$ is ________
Consider the random process $X(t)=U+Vt,$Where $U$ is a zero-mean Gaussian random variable and V is a ...
admin
46.4k
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116
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admin
asked
Nov 23, 2017
Probability and Statistics
gate2017-ec-2
numerical-answers
probability-and-statistics
probability
random-variable
uniform-distribution
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1
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0
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43
TIFR ECE 2014 | Question: 18
A non-negative loss in a car accident is distributed with the following probability density function \[ f(x)=\frac{1}{10} \exp (-x / 10) \] for $x \geq 0$. Suppose that first $5$ units of loss is incurred by the insured and the remaining loss if any is covered by the ... $5+10 \exp \left(-\frac{1}{2}\right)$ $15 \exp \left(-\frac{1}{2}\right)$
A non-negative loss in a car accident is distributed with the following probability density function\[f(x)=\frac{1}{10} \exp (-x / 10)\]for $x \geq 0$. Suppose that first...
admin
46.4k
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114
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admin
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Dec 14, 2022
Probability and Statistics
tifr2014
probability-and-statistics
probability
probability-density-function
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1
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44
TIFR ECE 2018 | Question: 12
Suppose that Amitabh Bachchan has ten coins in his pocket. $3$ coins have tails on both sides. $4$ coins have heads on both sides. $3$ coins have heads on one side and tails on the other and both the outcomes are equally likely when that coin is flipped. In a bet with Dharmendra ... that the other side of this coin is heads? $1 / 2$ $3 / 10$ $1 / 4$ $0.3$ $1 / 3$
Suppose that Amitabh Bachchan has ten coins in his pocket. $3$ coins have tails on both sides. $4$ coins have heads on both sides. $3$ coins have heads on one side and ta...
admin
46.4k
points
113
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admin
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Nov 29, 2022
Probability and Statistics
tifrece2018
probability-and-statistics
probability
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1
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45
TIFR ECE 2010 | Question: 16
Consider two independent random variables $\text{X}$ and $\text{Y}$ having probability density functions uniform in the interval $[0,1]$. The probability that $\text{X + Y}>1.5$ is $1 / 4$ $1 / 8$ $1 / 3$ $\operatorname{Pr}\{\text{X + Y} <0.25\}$ None of the above
Consider two independent random variables $\text{X}$ and $\text{Y}$ having probability density functions uniform in the interval $[0,1]$. The probability that $\text{X + ...
admin
46.4k
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112
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admin
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Probability and Statistics
tifr2010
probability-and-statistics
probability
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1
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46
TIFR ECE 2022 | Question: 7
Two players $\mathrm{A}$ and $\mathrm{B}$ of equal skill are playing a match. The first one to win $4$ rounds wins the match. Both players are equally likely to win each round independent of the outcomes of the other rounds. After $3$ rounds, $\mathrm{A}$ has won $2$ ... probability that $\mathrm{A}$ wins the match? $5 / 8$ $2 / 3$ $11 / 16$ $5 / 7$ None of the above
Two players $\mathrm{A}$ and $\mathrm{B}$ of equal skill are playing a match. The first one to win $4$ rounds wins the match. Both players are equally likely to win each ...
admin
46.4k
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111
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admin
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Nov 30, 2022
Probability and Statistics
tifrece2022
probability-and-statistics
probability
conditional-probability
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47
GATE2016 EC-3: 3
The probability of getting a “head” in a single toss of a biased coin is 0.3. The coin is tossed repeatedly till a “head” is obtained. If the tosses are independent, then the probability of getting “head” for the first time in the fifth toss is _________
The probability of getting a “head” in a single toss of a biased coin is 0.3. The coin is tossed repeatedly till a “head” is obtained. If the tosses are independe...
KUSHAGRA गुप्ता
240
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111
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KUSHAGRA गुप्ता
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Nov 21, 2019
Probability and Statistics
gate2016-ec
probability
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48
GATE ECE 2015 Set 2 | Question: 52
Let $X\in \{0,1\}$ and $Y\in \{0,1\}$ be two independent binary random variables. If $P(X=0)=p$ and $P(Y=0)=q,$ then $P(X+Y\geq 1)$ is equal to $pq+(1-p)(1-q)$ $pq$ $p(1-q)$ $1-pq$
Let $X\in \{0,1\}$ and $Y\in \{0,1\}$ be two independent binary random variables. If $P(X=0)=p$ and $P(Y=0)=q,$ then $P(X+Y\geq 1)$ is equal to$pq+(1-p)(1-q)$$pq$$p(1-q)$...
Milicevic3306
16.0k
points
108
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2015-ec-2
probability-and-statistics
probability
random-variable
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0
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49
GATE ECE 2014 Set 1 | Question: 50
Consider a random process $X(t) = \sqrt{2}\sin(2\pi t + \varphi),$ where the random phase $\varphi$ is uniformly distributed in the interval $[0,2\pi].$ The auto-correlation $E[X(t_{1})X(t_{2})]$ is $\cos(2\pi(t_{1} + t_{2}))$ $\sin(2\pi(t_{1} - t_{2}))$ $\sin(2\pi(t_{1} + t_{2}))$ $\cos(2\pi(t_{1} - t_{2}))$
Consider a random process $X(t) = \sqrt{2}\sin(2\pi t + \varphi),$ where the random phase $\varphi$ is uniformly distributed in the interval $[0,2\pi].$ The auto-correlat...
Milicevic3306
16.0k
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108
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Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2014-ec-1
probability-and-statistics
statistics
uniform-distribution
correlation-and-regression-analysis
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0
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0
answers
50
GATE ECE 2015 Set 3 | Question: 27
A fair die with faces $\{1, 2, 3, 4, 5, 6\}$ is thrown repeatedly till $’3’$ is observed for the first time. Let $X$ denote the number of times the die is thrown. The expected value of $X$ is _______.
A fair die with faces $\{1, 2, 3, 4, 5, 6\}$ is thrown repeatedly till $’3’$ is observed for the first time. Let $X$ denote the number of times the die is thrown. The...
Milicevic3306
16.0k
points
107
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2015-ec-3
numerical-answers
probability-and-statistics
probability
expectation
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answers
51
GATE ECE 2015 Set 1 | Question: 3
Suppose $A$ and $B$ are two independent events with probabilities $P(A) \neq 0$ and $P(B) \neq 0$. Let $\overline{A}$ and $\overline{B}$ be their complements. Which one of the following statements is FALSE? $P(A \cap B) = P(A)P(B)$ $P(A \mid B) = P(A)$ $P(A \cup B) = P(A) + P(B)$ $P(\overline{A} \cap \overline{B} )= P(\overline{A})P(\overline{B})$
Suppose $A$ and $B$ are two independent events with probabilities $P(A) \neq 0$ and $P(B) \neq 0$. Let $\overline{A}$ and $\overline{B}$ be their complements. Which one o...
Milicevic3306
16.0k
points
106
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2015-ec-1
probability-and-statistics
probability
independent-events
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0
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0
answers
52
GATE ECE 2014 Set 2 | Question: 2
Let $X$ be a random variable which is uniformly chosen from the set of positive odd numbers less than $100$. The expectation, $E[X]$, is ________.
Let $X$ be a random variable which is uniformly chosen from the set of positive odd numbers less than $100$. The expectation, $E[X]$, is ________.
Milicevic3306
16.0k
points
105
views
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2014-ec-2
probability-and-statistics
probability
uniform-distribution
random-variable
numerical-answers
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0
votes
0
answers
53
GATE ECE 2015 Set 2 | Question: 29
Let the random variable $X$ represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of $X$ is _______.
Let the random variable $X$ represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of $X$ is _...
Milicevic3306
16.0k
points
104
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2015-ec-2
numerical-answers
probability-and-statistics
probability
random-variable
expectation
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1
votes
0
answers
54
TIFR ECE 2014 | Question: 3
For a non-negative continuous random variable $X$, which of the following is TRUE? $E\{X\}=\int_{0}^{\infty} P(X>x) d x$. $E\{X\}=\int_{0}^{\infty} P(X \leq x) d x$. $P(X<x) \leq \frac{E\{X\}}{x}$. $(a)$ and $(c)$. None of the above.
For a non-negative continuous random variable $X$, which of the following is TRUE?$E\{X\}=\int_{0}^{\infty} P(X>x) d x$.$E\{X\}=\int_{0}^{\infty} P(X \leq x) d x$.$P(X<x)...
admin
46.4k
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102
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admin
asked
Dec 14, 2022
Probability and Statistics
tifr2014
probability-and-statistics
probability
random-variable
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1
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0
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55
TIFR ECE 2014 | Question: 14
Suppose that a random variable $X$ has a probability density function \[ \begin{aligned} f(x) & =c(x-4) \quad \text { for } 4 \leq x \leq 6 \\ & =0 \quad \text { for all other } x \end{aligned} \] for some constant $c$. What is the expected value of $X$ given that $X \geq 5?$ $5 \frac{5}{9}$ $5 \frac{1}{2}$ $5 \frac{3}{4}$ $5 \frac{1}{4}$ $5 \frac{5}{8}$
Suppose that a random variable $X$ has a probability density function\[\begin{aligned}f(x) & =c(x-4) \quad \text { for } 4 \leq x \leq 6 \\& =0 \quad \text { for all othe...
admin
46.4k
points
101
views
admin
asked
Dec 14, 2022
Probability and Statistics
tifr2014
probability-and-statistics
probability
probability-density-function
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0
votes
0
answers
56
GATE ECE 2014 Set 2 | Question: 49
The input to a $1$ – bit quantizer is a random variable $X$ with pdf $f_{X}( x )= 2e^{-2x}$ for $x\geq 0$ and $f_{X} (x )= 0$ for $x< 0$. For outputs to be of equal probability, the quantizer threshold should be ______.
The input to a $1$ – bit quantizer is a random variable $X$ with pdf $f_{X}( x )= 2e^{-2x}$ for $x\geq 0$ and $f_{X} (x )= 0$ for $x< 0$. For outputs to be of equal pro...
Milicevic3306
16.0k
points
101
views
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2014-ec-2
numerical-answers
probability-and-statistics
probability
probability-density-function
random-variable
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–
0
votes
0
answers
57
GATE ECE 2012 | Question: 24
Two independent random variables $X$ and $Y$ are uniformly distributed in the interval $[-1,1]$. The probability that max$[X,Y]$ is less than $\frac{1}{2}$ is $\frac{3}{4}$ $\frac{9}{16}$ $\frac{1}{4}$ $\frac{2}{3}$
Two independent random variables $X$ and $Y$ are uniformly distributed in the interval $[-1,1]$. The probability that max$[X,Y]$ is less than $\frac{1}{2}$ is$\frac{3}{4}...
Milicevic3306
16.0k
points
101
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2012-ec
probability-and-statistics
probability
independent-events
random-variable
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1
votes
0
answers
58
TIFR ECE 2015 | Question: 8
Let $X$ and $Y$ be two independent and identically distributed random variables. Let $Z=\max (X, Y)$ and $W=\min (X, Y)$. Which of the following is true? $Z$ and $W$ are independent $E(X Z)=E(Y W)$ $E(X Y)=E(Z W)$ $(a), (b)$, and $(c)$ $(a)$ and $(b)$ only
Let $X$ and $Y$ be two independent and identically distributed random variables. Let $Z=\max (X, Y)$ and $W=\min (X, Y)$. Which of the following is true?$Z$ and $W$ are i...
admin
46.4k
points
100
views
admin
asked
Dec 15, 2022
Probability and Statistics
tifr2015
probability-and-statistics
probability
random-variable
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1
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0
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59
TIFR ECE 2020 | Question: 7
Given $n$ independent Bernoulli random variables, taking value $1$ with probability $p$ and $0$ with probability $1-p$. Then, which of the following is the value of $E\left[\left(z_{1}+\right.\right.$ $\left.\left.\ldots z_{n}\right)^{2}\right] ?$ $0$ $n p+n(n-1) p^{2}$ $n^{3} p^{2}$ $n^{2} p^{2}+n p$ None of the above
Given $n$ independent Bernoulli random variables, taking value $1$ with probability $p$ and $0$ with probability $1-p$. Then, which of the following is the value of $E\le...
admin
46.4k
points
100
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2020
probability-and-statistics
probability
random-variable
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1
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0
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60
TIFR ECE 2018 | Question: 10
Suppose that $X_{1}$ and $X_{2}$ denote the random outcomes of independent rolls of two dice each of which takes six values $1,2,3,4,5,6$ with equal probability. What is the conditional expectation \[E\left[X_{1} \mid \max \left(X_{1}, X_{2}\right)=5\right]\] $3$ $4$ $35 / 9$ $5 / 2$ $15 / 4$
Suppose that $X_{1}$ and $X_{2}$ denote the random outcomes of independent rolls of two dice each of which takes six values $1,2,3,4,5,6$ with equal probability. What is ...
admin
46.4k
points
100
views
admin
asked
Nov 29, 2022
Probability and Statistics
tifrece2018
probability-and-statistics
probability
expectation
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–
1
votes
0
answers
61
TIFR ECE 2016 | Question: 3
Let $(X, Y)$ be a pair of independent random variables. Suppose $X$ takes values in $\{1, \ldots, 6\}$ with equal probability, and $Y$ takes values in $\{2,3\}$ with $\operatorname{Pr}[Y=2]=p$. Let $Z=(X \bmod Y)+1$ ... $\operatorname{Pr}[Z=1]=\frac{1}{2}$ for $p=\frac{1}{2}$ $\operatorname{Pr}[Z=1]=p(1-p)$ None of the above
Let $(X, Y)$ be a pair of independent random variables. Suppose $X$ takes values in $\{1, \ldots, 6\}$ with equal probability, and $Y$ takes values in $\{2,3\}$ with $\op...
admin
46.4k
points
100
views
admin
asked
Nov 29, 2022
Probability and Statistics
tifrece2016
probability-and-statistics
probability
random-variable
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1
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0
answers
62
TIFR ECE 2016 | Question: 7
Suppose $X$ and $Y$ are independent Gaussian random variables, whose pdfs are represented below. Which of the following describes the pdf of the $X+Y?$
Suppose $X$ and $Y$ are independent Gaussian random variables, whose pdfs are represented below. Which of the following describes the pdf of the $X+Y?$
admin
46.4k
points
100
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admin
asked
Nov 29, 2022
Probability and Statistics
tifrece2016
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63
TIFR ECE 2015 | Question: 9
Consider a random variable $X$ that takes integer values $1$ through $10$ each with equal probability. Now consider random variable \[ Y=\min (7, \max (X, 4)). \] What is the variance of $Y?$ $121 / 4$ $37 / 20 $ $9 / 5$ $99 / 12$ None of the above
Consider a random variable $X$ that takes integer values $1$ through $10$ each with equal probability. Now consider random variable\[Y=\min (7, \max (X, 4)).\]What is the...
admin
46.4k
points
99
views
admin
asked
Dec 15, 2022
Probability and Statistics
tifr2015
probability-and-statistics
probability
random-variable
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1
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0
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64
TIFR ECE 2020 | Question: 8
Suppose that Dice $1$ has five faces numbered $1$ to $5,$ each of which is equally likely to occur once the dice is rolled. Dice $2$ similarly has eight equally likely faces numbered $1$ to $8.$ Suppose that the two dice are rolled, and the sum is equal to $8.$ Conditioned on this, ... $2?$ $1 / 4$ $1 / 3$ $1 / 2$ $2 / 7$ $2 / 5$
Suppose that Dice $1$ has five faces numbered $1$ to $5,$ each of which is equally likely to occur once the dice is rolled. Dice $2$ similarly has eight equally likely fa...
admin
46.4k
points
97
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2020
probability-and-statistics
probability
conditional-probability
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–
1
votes
0
answers
65
TIFR ECE 2011 | Question: 9
Consider two independent random variables $X$ and $Y$ having probability density functions uniform in the interval $[-1,1]$. The probability that $X^{2}+Y^{2}>1$ is $\pi / 4$ $1-\pi / 4$ $\pi / 2-1$ Probability that $X^{2}+Y^{2}<0.5$ None of the above
Consider two independent random variables $X$ and $Y$ having probability density functions uniform in the interval $[-1,1]$. The probability that $X^{2}+Y^{2}>1$ is$\pi /...
admin
46.4k
points
96
views
admin
asked
Dec 5, 2022
Probability and Statistics
tifr2011
probability-and-statistics
probability
probability-density-function
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1
votes
0
answers
66
TIFR ECE 2012 | Question: 12
In modeling the number of health insurance claims filed by an individual during a three year period, an analyst makes a simplifying assumption that for all non-negative integer up to $5$. \[ p_{n+1}=\frac{1}{2} p_{n} \] where $p_{n}$ denotes the probability that a ... files more than two claims in this period? $7 / 31$ $29 / 125$ $1 / 3$ $13 / 125$ None of the above
In modeling the number of health insurance claims filed by an individual during a three year period, an analyst makes a simplifying assumption that for all non-negative i...
admin
46.4k
points
95
views
admin
asked
Dec 8, 2022
Probability and Statistics
tifr2012
probability-and-statistics
probability
conditional-probability
+
–
1
votes
0
answers
67
TIFR ECE 2018 | Question: 11
Assume the following well known result: If a coin is flipped independently many times and its probability of heads $(H)$ is $p \in(0,1)$ and probability of tails $(T)$ is $(1-p)$, then the expected number of coin flips till the first time a heads is observed is $1 / p$. What is the ... $\frac{1}{1-(1-p)^{2}}(4+1 / p)$ $\frac{1}{p}+\frac{1}{1-p}$
Assume the following well known result: If a coin is flipped independently many times and its probability of heads $(H)$ is $p \in(0,1)$ and probability of tails $(T)$ is...
admin
46.4k
points
95
views
admin
asked
Nov 29, 2022
Probability and Statistics
tifrece2018
probability-and-statistics
probability
expectation
+
–
0
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0
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68
GATE ECE 2016 Set 1 | Question: 2
The second moment of a Poisson-distributed random variable is $2$. The mean of the random variable is _____
The second moment of a Poisson-distributed random variable is $2$. The mean of the random variable is _____
Milicevic3306
16.0k
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95
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Milicevic3306
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Mar 27, 2018
Probability and Statistics
gate2016-ec-1
numerical-answers
probability-and-statistics
probability
poisson-distribution
random-variable
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–
1
votes
0
answers
69
TIFR ECE 2018 | Question: 7
Let $X_{1}, X_{2}$ and $X_{3}$ be independent random variables with uniform distribution over $[0, \theta]$. Consider the following statements. $E\left[\max \left\{X_{1}, X_{2}, X_{3}\right\}\right]=\frac{3}{4} \theta$ ... $\text{(i)}$ Only $\text{(ii)}$ Only $\text{(iii)}$ Only $\text{(iv)}$ All of $\text{(i) - (iv)}$
Let $X_{1}, X_{2}$ and $X_{3}$ be independent random variables with uniform distribution over $[0, \theta]$. Consider the following statements.$E\left[\max \left\{X_{1}, ...
admin
46.4k
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94
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admin
asked
Nov 29, 2022
Probability and Statistics
tifrece2018
probability-and-statistics
probability
uniform-distribution
+
–
1
votes
0
answers
70
TIFR ECE 2012 | Question: 13
Consider a single amoeba that at each time slot splits into two with probability $p$ or dies otherwise with probability $1-p$. This process is repeated independently infinitely at each time slot, i.e. if there are any amoebas left at time slot $t$, then they all split independently into ... $\min \left\{\frac{1 \pm \sqrt{1-4 p(1-p)}}{2(1-p)}\right\}$ None of the above
Consider a single amoeba that at each time slot splits into two with probability $p$ or dies otherwise with probability $1-p$. This process is repeated independently infi...
admin
46.4k
points
93
views
admin
asked
Dec 8, 2022
Probability and Statistics
tifr2012
probability-and-statistics
probability
independent-events
+
–
1
votes
0
answers
71
TIFR ECE 2015 | Question: 14
Consider a frog that lives on two rocks $A$ and $B$ and moves from one rock to the other randomly. If it is at Rock $A$ at any time, irrespective of which rocks it occupied in the past, it jumps back to Rock $A$ with probability $2 / 3$ and instead jumps to Rock ... of $n$ jumps as $n \rightarrow \infty?$ $1 / 2 $ $2 / 3$ $1$ The limit does not exist None of the above
Consider a frog that lives on two rocks $A$ and $B$ and moves from one rock to the other randomly. If it is at Rock $A$ at any time, irrespective of which rocks it occupi...
admin
46.4k
points
92
views
admin
asked
Dec 15, 2022
Probability and Statistics
tifr2015
probability-and-statistics
probability
conditional-probability
limits
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1
votes
0
answers
72
TIFR ECE 2014 | Question: 17
Let $X$ be a Gaussian random variable with mean $\mu_{1}$ and variance $\sigma_{1}^{2}$. Now, suppose that $\mu_{1}$ itself is a random variable, which is also Gaussian distributed with mean $\mu_{2}$ and variance $\sigma_{2}^{2}$. Then the distribution ... variable with mean $\mu_{2}$ and variance $\sigma_{1}^{2}+\sigma_{2}^{2}$. Has no known form. None of the above.
Let $X$ be a Gaussian random variable with mean $\mu_{1}$ and variance $\sigma_{1}^{2}$. Now, suppose that $\mu_{1}$ itself is a random variable, which is also Gaussian d...
admin
46.4k
points
92
views
admin
asked
Dec 14, 2022
Probability and Statistics
tifr2014
probability-and-statistics
probability
normal-distribution
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1
votes
0
answers
73
TIFR ECE 2010 | Question: 3
Consider two independent random variables $\text{X}$ and $\text{Y}$ having probability density functions uniform in the interval $[0,1]$. When $\alpha \geq 1$, the probability that $\max (\text{X, Y})>\alpha \min (\text{X, Y})$ is $1 /(2 \alpha)$ $\exp (1-\alpha)$ $1 / \alpha$ $1 / \alpha^{2}$ $1 / \alpha^{3}$
Consider two independent random variables $\text{X}$ and $\text{Y}$ having probability density functions uniform in the interval $[0,1]$. When $\alpha \geq 1$, the probab...
admin
46.4k
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92
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admin
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Nov 30, 2022
Probability and Statistics
tifr2010
probability-and-statistics
probability
probability-density-function
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–
1
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0
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74
TIFR ECE 2017 | Question: 10
Consider a single coin where the probability of heads is $p \in(0,1)$ and probability of tails is $1-p$. Suppose that this coin is flipped an infinite number of times. Let $N_{1}$ denote the number of flips till we see heads for the first time. Let $N_{2}$ denote the number of flips after ... $\frac{2}{p}$ $\frac{1}{p^{2}+(1-p)^{2}}$ $\frac{2}{p(1-p)}$
Consider a single coin where the probability of heads is $p \in(0,1)$ and probability of tails is $1-p$. Suppose that this coin is flipped an infinite number of times. Le...
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GATE ECE 2014 Set 3 | Question: 4
An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is $0.067$ $0.073$ $0.082$ $0.091$
An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is$0.067$$0.073$$0.082$$0.091$
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TIFR ECE 2015 | Question: 10
Let $X$ be a uniform random variable between $[0,1]$. And let \[ M=\min _{m X \geq 1, m \in \mathbb{N}} m . \] Then which of the following is true? $E(M)=\infty$ $E(M) \in[5,10]$ $E(M)=\exp (1)$ $E(M)=\pi$ None of the above
Let $X$ be a uniform random variable between $[0,1]$. And let\[M=\min _{m X \geq 1, m \in \mathbb{N}} m .\]Then which of the following is true?$E(M)=\infty$$E(M) \in[5,10...
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TIFR ECE 2011 | Question: 11
What is the value of $\lambda$ such that $\operatorname{Prob}\{X>\operatorname{mean}\{X\}\}=1 / e$, where $\text{PDF}$ of $X$ is $p_{X}(x)=\lambda e^{-\lambda x}, x \geq 0, \lambda>0?$ $1$ $1 / e$ $1 / \sqrt{e}$ $1 / e^{2}$ All of the above
What is the value of $\lambda$ such that $\operatorname{Prob}\{X>\operatorname{mean}\{X\}\}=1 / e$, where $\text{PDF}$ of $X$ is $p_{X}(x)=\lambda e^{-\lambda x}, x \geq ...
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TIFR ECE 2021 | Question: 11
Suppose that $X_{1}$ and $X_{2}$ denote the output of rolls of two independent dices that can each take integer values $\{1,2,3,4,5,6\}$ with probability $1 / 6$ for each outcome. Further, $U$ denotes a continuous random variable that is independent of $X_{1}$ and $X_{2}$ ... on this sum what is the probability that $X_{1}$ equals $2?$ $2.21$ $3$ $1 / 6$ $1 / 5$ $1 / 3$
Suppose that $X_{1}$ and $X_{2}$ denote the output of rolls of two independent dices that can each take integer values $\{1,2,3,4,5,6\}$ with probability $1 / 6$ for each...
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TIFR ECE 2018 | Question: 2
A hotel has $n$ rooms numbered $1,2, \ldots, n$. For each room there is one spare key labeled with the room number. The hotel manager keeps all the spare keys in a box. Her mischievous son got hold of the box and permuted the labels uniformly at random. What is the ... Use linearity of expectation] $1$ $\frac{n-1}{n}$ $\frac{n}{n-1}$ $\frac{n}{2}$ None of the above
A hotel has $n$ rooms numbered $1,2, \ldots, n$. For each room there is one spare key labeled with the room number. The hotel manager keeps all the spare keys in a box. H...
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80
TIFR ECE 2020 | Question: 3
Balls are drawn one after the other uniformly at random without replacement from a set of eight balls numbered $1,2, \ldots, 8$ until all balls drawn. What is the expected number of balls whose value match their ordinality (i.e., their position in the order in which ... ? Now can you use linearity of expectation to solve the problem? $1$ $1.5$ $2$ $2.5$ None of the above
Balls are drawn one after the other uniformly at random without replacement from a set of eight balls numbered $1,2, \ldots, 8$ until all balls drawn. What is the expecte...
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