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Hot questions in Probability and Statistics
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81
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
points
111
views
KUSHAGRA गुप्ता
asked
Nov 21, 2019
Probability and Statistics
gate2016-ec
probability
+
–
1
votes
1
answer
82
GATE ECE 2014 Set 1 | Question: 2
In a housing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that a child picked at random, has a sibling is ________.
In a housing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that a child picked at r...
Milicevic3306
16.0k
points
757
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2014-ec-1
numerical-answers
probability-and-statistics
probability
+
–
0
votes
0
answers
83
GATE ECE 2019 | Question: 20
Let $Z$ be an exponential random variable with mean $1$. That is, the cumulative distribution function of $Z$ is given by $F_{Z}(x)= \left\{\begin{matrix} 1-e^{-x}& \text{if}\: x \geq 0 \\ 0& \text{if}\: x< 0 \end{matrix}\right.$ Then $Pr\left(Z>2 \mid Z>1\right),$ rounded off to two decimal places, is equal to ___________.
Let $Z$ be an exponential random variable with mean $1$. That is, the cumulative distribution function of $Z$ is given by$$F_{Z}(x)= \left\{\begin{matrix} 1-e^{-x}& \text...
Arjun
6.6k
points
236
views
Arjun
asked
Feb 12, 2019
Probability and Statistics
gate2019-ec
numerical-answers
probability-and-statistics
probability
random-variable
+
–
0
votes
0
answers
84
GATE ECE 2019 | Question: 47
A random variable $X$ takes values $-1$ and $+1$ with probabilities $0.2$ and $0.8$, respectively. It is transmitted across a channel which adds noise $N,$ so that the random variable at the channel output is $Y=X+N$. The noise $N$ is ... probability of error $Pr[ \hat{X} \neq X].$ The minimum probability of error, rounded off to $1$ decimal place, is _________.
A random variable $X$ takes values $-1$ and $+1$ with probabilities $0.2$ and $0.8$, respectively. It is transmitted across a channel which adds noise $N,$ so that the ra...
Arjun
6.6k
points
193
views
Arjun
asked
Feb 12, 2019
Probability and Statistics
gate2019-ec
numerical-answers
probability-and-statistics
probability
random-variable
uniform-distribution
+
–
0
votes
0
answers
85
GATE ECE 2019 | Question: 18
If $X$ and $Y$ are random variables such that $E\left[2X+Y\right]=0$ and $E\left[X+2Y\right]=33$, then $E\left[X\right]+E\left[Y\right]=$___________.
If $X$ and $Y$ are random variables such that $E\left[2X+Y\right]=0$ and $E\left[X+2Y\right]=33$, then $E\left[X\right]+E\left[Y\right]=$___________.
Arjun
6.6k
points
153
views
Arjun
asked
Feb 12, 2019
Probability and Statistics
gate2019-ec
numerical-answers
probability-and-statistics
probability
random-variable
expectation
+
–
0
votes
1
answer
86
GATE ECE 2012 | Question: 36
A fair coin is tossed till head appears for the first time. The probability that the number of required tosses is odd, is $\frac{1}{3}$ $\frac{1}{2}$ $\frac{2}{3}$ $\frac{3}{4}$
A fair coin is tossed till head appears for the first time. The probability that the number of required tosses is odd, is$\frac{1}{3}$$\frac{1}{2}$$\frac{2}{3}$$\frac{3}{...
Milicevic3306
16.0k
points
179
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2012-ec
probability-and-statistics
probability
+
–
0
votes
0
answers
87
GATE ECE 2016 Set 3 | Question: 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 independent, ...
Milicevic3306
16.0k
points
222
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2016-ec-3
probability-and-statistics
probability
independent-events
+
–
0
votes
0
answers
88
GATE ECE 2016 Set 3 | Question: 51
The bit error probability of a memoryless binary symmetric channel is $10^{-5}$. If $10^5$ bits are sent over this channel, then the probability that not more than one bit will be in error is _______
The bit error probability of a memoryless binary symmetric channel is $10^{-5}$. If $10^5$ bits are sent over this channel, then the probability that not more than one bi...
Milicevic3306
16.0k
points
215
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2016-ec-3
numerical-answers
probability-and-statistics
probability
+
–
0
votes
0
answers
89
GATE ECE 2015 Set 1 | Question: 49
The input $X$ to the Binary Symmetric Channel (BSC) shown in the figure is $’1’$ with probability $0.8$. The cross-over probability is $1/7$. If the received bit $Y=0$, the conditional probability that $’1’$ was transmitted is ____________
The input $X$ to the Binary Symmetric Channel (BSC) shown in the figure is $’1’$ with probability $0.8$. The cross-over probability is $1/7$. If the received bit $Y=0...
Milicevic3306
16.0k
points
193
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2015-ec-1
numerical-answers
probability-and-statistics
probability
+
–
0
votes
0
answers
90
GATE ECE 2015 Set 3 | Question: 50
The variance of the random variable $X$ with probability density function $f(x)=\dfrac{1}{2}\mid x \mid e^{- \mid x \mid}$ is __________.
The variance of the random variable $X$ with probability density function $f(x)=\dfrac{1}{2}\mid x \mid e^{- \mid x \mid}$ is __________.
Milicevic3306
16.0k
points
186
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2015-ec-3
numerical-answers
probability-and-statistics
propability
random-variable
variance
+
–
0
votes
0
answers
91
GATE ECE 2016 Set 2 | Question: 28
Two random variables $X$ and $Y$ are distributed according to $f_{X,Y}(x,y)=\begin{cases} (x+y),& 0\leq x\leq 1,&0\leq y\leq 1\\ 0, & \text{otherwise.} \end{cases}$ The probability $P(X+Y\leq 1)$ is ________
Two random variables $X$ and $Y$ are distributed according to $$f_{X,Y}(x,y)=\begin{cases} (x+y),& 0\leq x\leq 1,&0\leq y\leq 1\\ 0, & \text{otherwise.} \end{cases}$$ The...
Milicevic3306
16.0k
points
183
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2016-ec-2
numerical-answers
probability-and-statistics
probability
probability-density-function
+
–
0
votes
0
answers
92
GATE ECE 2015 Set 1 | Question: 52
A source emits bit $0$ with probability $\frac{1}{3}$ and bit $1$ with probability $\frac{2}{3}$. The emitted bits are communicated to the receiver. The receiver decides for either $0$ or $1$ based on the received value $R$. It is given that the ... $0$ $1/12$ $1/9$ $1/6$
A source emits bit $0$ with probability $\frac{1}{3}$ and bit $1$ with probability $\frac{2}{3}$. The emitted bits are communicated to the receiver. The receiver decides ...
Milicevic3306
16.0k
points
161
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2015-ec-1
probability-and-statistics
probability
probability-density-function
+
–
0
votes
0
answers
93
GATE ECE 2013 | Question: 38
Consider two identically distributed zero-mean random variables $U$ and $V.$ Let the cumulative distribution functions of $U$ and $2V$ be $F(x)$ and $G(x)$ respectively. Then, for all values of $x$ $F(x) - G(x) \leq 0$ $F(x) - G(x) \geq 0$ $(F(x) - G(x)) \cdot x\leq 0$ $(F(x) - G(x)) \cdot x\geq 0$
Consider two identically distributed zero-mean random variables $U$ and $V.$ Let the cumulative distribution functions of $U$ and $2V$ be $F(x)$ and $G(x)$ respectively. ...
Milicevic3306
16.0k
points
235
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2013-ec
probability-and-statistics
probability
random-variable
+
–
0
votes
0
answers
94
GATE ECE 2016 Set 1 | Question: 48
Consider a discrete memoryless source with alphabet $S = \{s_0,s_1,s_2,s_3,s_4, \dots \}$ and respective probabilities of occurence $P = \bigg\{ \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \frac{1}{32}, \dots \bigg\}$. The entropy of the source (in bits) is _________
Consider a discrete memoryless source with alphabet $S = \{s_0,s_1,s_2,s_3,s_4, \dots \}$ and respective probabilities of occurence $P = \bigg\{ \frac{1}{2}, \frac{1}{4},...
Milicevic3306
16.0k
points
150
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2016-ec-1
numerical-answers
probability-and-statistics
probability
+
–
0
votes
0
answers
95
GATE ECE 2016 Set 2 | Question: 21
A discrete memoryless source has an alphabet $\left \{ a_{1},a_{2}, a_{3},a_{4}\right \}$ with corresponding probabilities $\left \{ \frac{1}{2}, \frac{1}{4},\frac{1}{8},\frac{1}{8}\right \}.$ The minimum required average codeword length in bits to represent this source for error-free reconstruction is _________
A discrete memoryless source has an alphabet $\left \{ a_{1},a_{2}, a_{3},a_{4}\right \}$ with corresponding probabilities $\left \{ \frac{1}{2}, \frac{1}{4},\frac{1}{8},...
Milicevic3306
16.0k
points
143
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2016-ec-2
numerical-answers
probability-and-statistics
probability
+
–
0
votes
0
answers
96
GATE ECE 2015 Set 3 | Question: 52
A random binary wave $y(t)$ is given by $y(t) = \sum_{n = -\infty}^{\infty}X_{n}\:p(t-nT-\phi)$ where $p(t)=u(t)-u(t-T),u(t)$ is the unit step function and $\phi$ is an independent random variable with uniform distribution in $[0,T].$ ... $R_{yy}\left(\dfrac{3T}{4}\right) \underset{=}{\Delta} E\left[y(t)y\left(t-\dfrac{3T}{4}\right)\right]$ equals _________.
A random binary wave $y(t)$ is given by$$y(t) = \sum_{n = -\infty}^{\infty}X_{n}\:p(t-nT-\phi)$$where $p(t)=u(t)-u(t-T),u(t)$ is the unit step function and $\phi$ is an i...
Milicevic3306
16.0k
points
136
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2015-ec-3
numerical-answers
probability-and-statistics
probability
random-variable
uniform-distribution
+
–
0
votes
0
answers
97
GATE ECE 2012 | Question: 38
A binary symmetric channel (BSC) has a transition probability of $\frac{1}{8}$. If the binary transmit symbol $X$ is such that $P(X=0)\:=\:\frac{9}{10}$, then the probability of error for an optimum receiver will be $\frac{7}{80}$ $\frac{63}{80}$ $\frac{9}{10}$ $\frac{1}{10}$
A binary symmetric channel (BSC) has a transition probability of $\frac{1}{8}$. If the binary transmit symbol $X$ is such that $P(X=0)\:=\:\frac{9}{10}$, then the probabi...
Milicevic3306
16.0k
points
239
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2012-ec
probability-and-statistics
probability
+
–
0
votes
0
answers
98
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
+
–
0
votes
0
answers
99
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
+
–
0
votes
0
answers
100
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
+
–
0
votes
0
answers
101
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
+
–
0
votes
0
answers
102
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
points
95
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2016-ec-1
numerical-answers
probability-and-statistics
probability
poisson-distribution
random-variable
+
–
0
votes
0
answers
103
GATE ECE 2012 | Question: 15
A source alphabet consists of $N$ symbols with the probability of the first two symbols being the same. A source encoder increases the probability of the first symbol by a small amount $\varepsilon$ and decreases that of the second by $\varepsilon$. After encoding, the entropy of the source increases remains the same increases only if $N=2$ decreases
A source alphabet consists of $N$ symbols with the probability of the first two symbols being the same. A source encoder increases the probability of the first symbol by ...
Milicevic3306
16.0k
points
173
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2012-ec
probability-and-statistics
probability
+
–
0
votes
0
answers
104
GATE ECE 2014 Set 3 | Question: 29
Let $X_{1},X_{2},$ and $X_{3}$ be independent and identically distributed random variables with the uniform distribution on $[0,1]$. The probability $P\left \{ X_{1}+X_{2}\leq X_{3}\right \}$ is _________.
Let $X_{1},X_{2},$ and $X_{3}$ be independent and identically distributed random variables with the uniform distribution on $[0,1]$. The probability $P\left \{ X_{1}+X_{2...
Milicevic3306
16.0k
points
135
views
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2014-ec-3
probability-and-statistics
probability
independent-events
random-variable
uniform-distribution
numerical-answers
+
–
0
votes
0
answers
105
GATE ECE 2013 | Question: 26
Let $U$ and $V$ be two independent zero mean Gaussian random variables of variances $\dfrac{1}{4}$ and $\dfrac{1}{9}$ respectively. The probability $P(3V\geq 2U)$ is $4/9$ $1/2$ $2/3$ $5/9$
Let $U$ and $V$ be two independent zero mean Gaussian random variables of variances $\dfrac{1}{4}$ and $\dfrac{1}{9}$ respectively. The probability $P(3V\geq 2U)$ is$4/9$...
Milicevic3306
16.0k
points
139
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2013-ec
probability-and-statistics
probability
random-variable
independent-events
+
–
0
votes
0
answers
106
GATE ECE 2014 Set 3 | Question: 52
A binary random variable $X$ takes the value of $1$ with probability $1/3$. $X$ is input to a cascade of $2$ independent identical binary symmetric channels (BSCs) each with crossover probability $1/2$. The output of BSCs are the random variables $Y_{1}$ and $Y_{2}$ as shown in the figure. The value of $H( Y_{1} )+H( Y_{2} )$ in bits is ______.
A binary random variable $X$ takes the value of $1$ with probability $1/3$. $X$ is input to a cascade of $2$ independent identical binary symmetric channels (BSCs) each w...
Milicevic3306
16.0k
points
132
views
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2014-ec-3
probability-and-statistics
probability
numerical-answers
+
–
0
votes
0
answers
107
GATE ECE 2014 Set 4 | Question: 27
Parcels from sender S to receiver R pass sequentially through two-post offices. Each post-office has a probability $\frac{1}{5}$ of losing an incoming parcel, independently of all other parcels. Given that a parcel is lost, the probability that it was lost by the second post office is _________
Parcels from sender S to receiver R pass sequentially through two-post offices. Each post-office has a probability $\frac{1}{5}$ of losing an incoming parcel, independent...
Milicevic3306
16.0k
points
127
views
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2014-ec-4
numerical-answers
probability-and-statistics
probability
+
–
0
votes
0
answers
108
GATE ECE 2014 Set 1 | Question: 5
Let $X_{1},X_{2},$ and $X_{3}$ be independent and identically distributed random variables with the uniform distribution on $[0,1].$ The probability $P\{X_{1}\: \text{is the largest}\}$ is ________.
Let $X_{1},X_{2},$ and $X_{3}$ be independent and identically distributed random variables with the uniform distribution on $[0,1].$ The probability $P\{X_{1}\: \text{is ...
Milicevic3306
16.0k
points
119
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2014-ec-1
numerical-answers
probability-and-statistics
probability
uniform-distribution
+
–
0
votes
0
answers
109
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
points
108
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2014-ec-1
probability-and-statistics
statistics
uniform-distribution
correlation-and-regression-analysis
+
–
0
votes
0
answers
110
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
+
–
0
votes
0
answers
111
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
+
–
0
votes
0
answers
112
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$
Milicevic3306
16.0k
points
92
views
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2014-ec-3
probability-and-statistics
probability
+
–
0
votes
0
answers
113
GATE ECE 2014 Set 4 | Question: 50
Consider the $Z$-channel given in the figure. The input is $0$ or $1$ with equal probability. If the output is $0$, the probability that the input is also $0$ equals ___________
Consider the $Z$-channel given in the figure. The input is $0$ or $1$ with equal probability.If the output is $0$, the probability that the input is also $0$ equals _____...
Milicevic3306
16.0k
points
87
views
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2014-ec-4
numerical-answers
probability-and-statistics
probability
+
–
0
votes
0
answers
114
GATE ECE 2014 Set 3 | Question: 28
A fair coin is tossed repeatedly till both head and tail appear at least once. The average number of tosses required is _______ .
A fair coin is tossed repeatedly till both head and tail appear at least once. The average number of tosses required is _______ .
Milicevic3306
16.0k
points
87
views
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2014-ec-3
probability-and-statistics
probability
expectation
numerical-answers
+
–
0
votes
0
answers
115
GATE ECE 2014 Set 1 | Question: 49
Let $X$ be a real-valued random variable with $E[X]$ and $E[X^{2}]$ denoting the mean values of $X$ and $X^{2},$ respectively. The relation which always holds true is $(E[X])^{2}>E[X^{2}]$ $E[X^{2}]\geq (E[X])^{2}$ $E[X^{2}] = (E[X])^{2}$ $E[X^{2}] > (E[X])^{2}$
Let $X$ be a real-valued random variable with $E[X]$ and $E[X^{2}]$ denoting the mean values of $X$ and $X^{2},$ respectively. The relation which always holds true is$(E[...
Milicevic3306
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gate2014-ec-1
probability-and-statistics
probability
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expectation
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116
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
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Probability and Statistics
gate2012-ec
probability-and-statistics
probability
independent-events
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117
GATE ECE 2018 | Question: 40
A random variable $X$ takes values $-0.5$ and $0.5$ with probabilities $\dfrac{1}{4}$ and $\dfrac{3}{4}$, respectively. The noisy observation of $X\:\text{is}\:Y=X+Z,$ where $Z$ ... $\alpha$ (accurate to two decimal places) is ________.
A random variable $X$ takes values $-0.5$ and $0.5$ with probabilities $\dfrac{1}{4}$ and $\dfrac{3}{4}$, respectively. The noisy observation of $X\:\text{is}\:Y=X+Z,$ wh...
gatecse
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Feb 19, 2018
Probability and Statistics
gate2018-ec
numerical-answers
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propability
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118
GATE ECE 2018 | Question: 23
Let $X_{1},\:X_{2},\:X_{3}$ and $X_{4}$ be independent normal random variable with zero mean and unit variance. The probability that $X_{4}$ is the smallest among the four is ________.
Let $X_{1},\:X_{2},\:X_{3}$ and $X_{4}$ be independent normal random variable with zero mean and unit variance. The probability that $X_{4}$ is the smallest among the fou...
gatecse
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159
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Feb 19, 2018
Probability and Statistics
gate2018-ec
numerical-answers
probability-and-statistics
probability
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variance
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1
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0
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119
GATE ECE 2017 Set 2 | Question: 29
Passengers try repeatedly to get a seat reservation in any train running between two stations until they are successful. If there is $40 \%$ chance of getting reservation in any attempt by a passenger, then the average number of attempts that passengers need to make to get a seat reserved is __________
Passengers try repeatedly to get a seat reservation in any train running between two stations until they are successful. If there is $40 \%$ chance of getting reservation...
admin
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admin
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Nov 23, 2017
Probability and Statistics
gate2017-ec-2
numerical-answers
probability-and-statistics
probability
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0
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0
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120
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
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Nov 23, 2017
Probability and Statistics
gate2017-ec-2
numerical-answers
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probability
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