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Recent questions tagged probability
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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
109
views
KUSHAGRA गुप्ता
asked
Nov 21, 2019
Probability and Statistics
gate2016-ec
probability
+
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0
votes
0
answers
82
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
152
views
Arjun
asked
Feb 12, 2019
Probability and Statistics
gate2019-ec
numerical-answers
probability-and-statistics
probability
random-variable
expectation
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0
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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
235
views
Arjun
asked
Feb 12, 2019
Probability and Statistics
gate2019-ec
numerical-answers
probability-and-statistics
probability
random-variable
+
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0
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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
190
views
Arjun
asked
Feb 12, 2019
Probability and Statistics
gate2019-ec
numerical-answers
probability-and-statistics
probability
random-variable
uniform-distribution
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0
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0
answers
85
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
219
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2016-ec-3
probability-and-statistics
probability
independent-events
+
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0
votes
0
answers
86
GATE ECE 2016 Set 3 | Question: 22
An analog baseband signal, bandlimited to $100\ Hz$, is sampled at the Nyquist rate. The samples are quantized into four message symbols that occur independently with probabilities $p_1 = p_4 = 0.125$ and $p_2 = p_3$. The information rate (bits/sec) of the message source is _______
An analog baseband signal, bandlimited to $100\ Hz$, is sampled at the Nyquist rate. The samples are quantized into four message symbols that occur independently with pro...
Milicevic3306
16.0k
points
111
views
Milicevic3306
asked
Mar 27, 2018
Control Systems
gate2016-ec-3
numerical-answers
control-systems
nyquist
probability
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0
votes
0
answers
87
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
213
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2016-ec-3
numerical-answers
probability-and-statistics
probability
+
–
0
votes
0
answers
88
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
142
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2016-ec-2
numerical-answers
probability-and-statistics
probability
+
–
0
votes
0
answers
89
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
182
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
90
GATE ECE 2016 Set 1 | GA Question: 6
A person moving through a tuberculosis prone zone has a $50 \%$ probability of becoming infected. However, only $30 \%$ of infected people develop the disease. What percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease? $15$ $33$ $35$ $37$
A person moving through a tuberculosis prone zone has a $50 \%$ probability of becoming infected. However, only $30 \%$ of infected people develop the disease. What perce...
Milicevic3306
16.0k
points
105
views
Milicevic3306
asked
Mar 27, 2018
Quantitative Aptitude
gate2016-ec-1
numerical-ability
probability
+
–
0
votes
0
answers
91
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
94
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2016-ec-1
numerical-answers
probability-and-statistics
probability
poisson-distribution
random-variable
+
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0
votes
0
answers
92
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
146
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2016-ec-1
numerical-answers
probability-and-statistics
probability
+
–
0
votes
0
answers
93
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
106
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2015-ec-3
numerical-answers
probability-and-statistics
probability
expectation
+
–
0
votes
0
answers
94
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)$$where $p(t)=u(t)-u(t-T),u(t)$ is the unit step function and $\phi$ is an i...
Milicevic3306
16.0k
points
136
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2015-ec-3
numerical-answers
probability-and-statistics
probability
random-variable
uniform-distribution
+
–
0
votes
0
answers
95
GATE ECE 2015 Set 2 | GA Question: 5
Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram's selection is $1/6$ and that of Ramesh is $1/8$. What is the probability that only one of them will be selected? $47/48$ $1/4$ $13/48$ $35/48$
Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram's selection is $1/6$ and that of Ramesh is $1/8$. What is the pro...
Milicevic3306
16.0k
points
97
views
Milicevic3306
asked
Mar 27, 2018
Quantitative Aptitude
gate2015-ec-2
numerical-ability
probability
+
–
0
votes
0
answers
96
GATE ECE 2015 Set 2 | Question: 29
Let the random variable $X$ represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of $X$ is _______.
Let the random variable $X$ represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of $X$ is _...
Milicevic3306
16.0k
points
103
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2015-ec-2
numerical-answers
probability-and-statistics
probability
random-variable
expectation
+
–
0
votes
0
answers
97
GATE ECE 2015 Set 2 | Question: 52
Let $X\in \{0,1\}$ and $Y\in \{0,1\}$ be two independent binary random variables. If $P(X=0)=p$ and $P(Y=0)=q,$ then $P(X+Y\geq 1)$ is equal to $pq+(1-p)(1-q)$ $pq$ $p(1-q)$ $1-pq$
Let $X\in \{0,1\}$ and $Y\in \{0,1\}$ be two independent binary random variables. If $P(X=0)=p$ and $P(Y=0)=q,$ then $P(X+Y\geq 1)$ is equal to$pq+(1-p)(1-q)$$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
98
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
105
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2015-ec-1
probability-and-statistics
probability
independent-events
+
–
0
votes
0
answers
99
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
191
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2015-ec-1
numerical-answers
probability-and-statistics
probability
+
–
0
votes
0
answers
100
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
159
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2015-ec-1
probability-and-statistics
probability
probability-density-function
+
–
0
votes
0
answers
101
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
126
views
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2014-ec-4
numerical-answers
probability-and-statistics
probability
+
–
0
votes
0
answers
102
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
103
GATE ECE 2014 Set 3 | GA Question: 10
A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batch is rejected if even one of the bulbs is defective. A batch typically has five defective bulbs. The probability that the current batch is accepted is ________
A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batch is rejected if even one of the bulbs is defective. A batch typically has five d...
Milicevic3306
16.0k
points
74
views
Milicevic3306
asked
Mar 26, 2018
Quantitative Aptitude
gate2014-ec-3
numerical-ability
probability
numerical-answers
+
–
0
votes
0
answers
104
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
91
views
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2014-ec-3
probability-and-statistics
probability
+
–
0
votes
0
answers
105
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
85
views
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2014-ec-3
probability-and-statistics
probability
expectation
numerical-answers
+
–
0
votes
0
answers
106
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
134
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
107
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
131
views
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2014-ec-3
probability-and-statistics
probability
numerical-answers
+
–
0
votes
0
answers
108
GATE ECE 2014 Set 2 | GA Question: 4
A regular die has six sides with numbers $1$ to $6$ marked on its sides. If a very large number of throws show the following frequencies of occurrence: $1 \rightarrow 0.167$; $2 \rightarrow 0.167$; $3 \rightarrow 0.152$; $4 \rightarrow 0.166$; $5 \rightarrow 0.168$; $6 \rightarrow 0.180$. We call this die irregular biased Gaussian insufficient
A regular die has six sides with numbers $1$ to $6$ marked on its sides. If a very large number of throws show the following frequencies of occurrence: $1 \rightarrow 0.1...
Milicevic3306
16.0k
points
90
views
Milicevic3306
asked
Mar 26, 2018
Quantitative Aptitude
gate2014-ec-2
numerical-ability
probability
+
–
0
votes
0
answers
109
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
110
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
111
GATE ECE 2014 Set 1 | GA Question: 10
You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is $1/4$ $1/3$ $1/2$ $2/3$
You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coi...
Milicevic3306
16.0k
points
78
views
Milicevic3306
asked
Mar 25, 2018
Quantitative Aptitude
gate2014-ec-1
numerical-ability
probability
+
–
1
votes
1
answer
112
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
754
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2014-ec-1
numerical-answers
probability-and-statistics
probability
+
–
0
votes
0
answers
113
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
118
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2014-ec-1
numerical-answers
probability-and-statistics
probability
uniform-distribution
+
–
0
votes
0
answers
114
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
16.0k
points
82
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2014-ec-1
probability-and-statistics
probability
random-variable
expectation
+
–
0
votes
0
answers
115
GATE ECE 2013 | Question: 65
What is the chance that a leap year, selected at random, will contain $53$ Saturdays? $2/7$ $3/7$ $1/7$ $5/7$
What is the chance that a leap year, selected at random, will contain $53$ Saturdays?$2/7$$3/7$$1/7$$5/7$
Milicevic3306
16.0k
points
110
views
Milicevic3306
asked
Mar 25, 2018
Quantitative Aptitude
gate2013-ec
numerical-ability
probability
leap-year
+
–
0
votes
0
answers
116
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
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232
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Milicevic3306
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Mar 25, 2018
Probability and Statistics
gate2013-ec
probability-and-statistics
probability
random-variable
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0
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0
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117
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
138
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2013-ec
probability-and-statistics
probability
random-variable
independent-events
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0
votes
0
answers
118
GATE ECE 2012 | Question: 65
$A$ and $B$ are friends. They decide to meet between $1:00$pm and $2:00$ pm on a given day. There is a condition that whoever arrives first will not wait for the other for more than $15$ minutes. The probability that they will meet on that day is $1/4$ $1/16$ $7/16$ $9/16$
$A$ and $B$ are friends. They decide to meet between $1:00$pm and $2:00$ pm on a given day. There is a condition that whoever arrives first will not wait for the other fo...
Milicevic3306
16.0k
points
96
views
Milicevic3306
asked
Mar 25, 2018
Quantitative Aptitude
gate2012-ec
numerical-ability
probability
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–
0
votes
0
answers
119
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
1
answer
120
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
178
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2012-ec
probability-and-statistics
probability
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