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Recent questions tagged randomvariable
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GATE ECE 2021  Question: 3
Two continuous random variables $X$ and $Y$ are related as $Y=2X+3$ Let $\sigma ^{2}_{X}$ and $\sigma ^{2}_{Y}$denote the variances of $X$ and $Y$, respectively. The variances are related as $\sigma ^{2}_{Y}=2 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=4 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=5 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=25 \sigma ^{2}_{X}$
asked
Feb 20
in
Probability and Statistics
by
Arjun
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4.5k
points)

38
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gateec2021
probabilityandstatistics
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variance
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2
GATE ECE 2020  Question: 25
The two sides of a fair coin are labelled as $0$ to $1$. The coin is tossed two times independently. Let $M$ and $N$ denote the labels corresponding to the outcomes of those tosses. For a random variable $X$, defined as $X = \text{min}(M, N)$, the expected value $E(X)$ (rounded off to two decimal places) is ___________.
asked
Feb 13, 2020
in
Probability and Statistics
by
jothee
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1.9k
points)

96
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gate2020ec
numericalanswers
probabilityandstatistics
probability
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expectation
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3
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 $E\left[X\right]+E\left[Y\right]=$___________.
asked
Feb 12, 2019
in
Probability and Statistics
by
Arjun
(
4.5k
points)

55
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gate2019ec
numericalanswers
probabilityandstatistics
probability
randomvariable
expectation
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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 $F_{Z}(x)= \left\{\begin{matrix} 1e^{x}& \text{if}\: x \geq 0 \\ 0& \text{if}\: x< 0 \end{matrix}\right.$ Then $Pr\left(Z>2 \mid Z>1\right),$ rounded off to two decimal places, is equal to ___________.
asked
Feb 12, 2019
in
Probability and Statistics
by
Arjun
(
4.5k
points)

115
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gate2019ec
numericalanswers
probabilityandstatistics
probability
randomvariable
0
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5
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 _________.
asked
Feb 12, 2019
in
Probability and Statistics
by
Arjun
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4.5k
points)

86
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gate2019ec
numericalanswers
probabilityandstatistics
probability
randomvariable
uniformdistribution
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0
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6
GATE ECE 2016 Set 1  Question: 2
The second moment of a Poissondistributed random variable is $2$. The mean of the random variable is _____
asked
Mar 28, 2018
in
Probability and Statistics
by
Milicevic3306
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15.8k
points)

26
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gate2016ec1
numericalanswers
probabilityandstatistics
probability
poissondistribution
randomvariable
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7
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 __________.
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Mar 28, 2018
in
Probability and Statistics
by
Milicevic3306
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15.8k
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40
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gate2015ec3
numericalanswers
probabilityandstatistics
propability
randomvariable
variance
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8
GATE ECE 2015 Set 3  Question: 52
A random binary wave $y(t)$ is given by $y(t) = \sum_{n = \infty}^{\infty}X_{n}\:p(tnT\phi)$ where $p(t)=u(t)u(tT),u(t)$ 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 _________.
asked
Mar 28, 2018
in
Probability and Statistics
by
Milicevic3306
(
15.8k
points)

25
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gate2015ec3
numericalanswers
probabilityandstatistics
probability
randomvariable
uniformdistribution
0
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0
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9
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 _______.
asked
Mar 28, 2018
in
Probability and Statistics
by
Milicevic3306
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15.8k
points)

21
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gate2015ec2
numericalanswers
probabilityandstatistics
probability
randomvariable
expectation
0
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10
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 $pq+(1p)(1q)$ $pq$ $p(1q)$ $1pq$
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Mar 28, 2018
in
Probability and Statistics
by
Milicevic3306
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15.8k
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21
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gate2015ec2
probabilityandstatistics
probability
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0
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11
GATE ECE 2014 Set 4  Question: 3
Let $X$ be a zero mean unit variance Gaussian random variable. $E[ \mid X \mid ]$ is equal to __________
asked
Mar 26, 2018
in
Vector Analysis
by
Milicevic3306
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15.8k
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28
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gate2014ec4
numericalanswers
vectoranalysis
gaussstheorem
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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 _________.
asked
Mar 26, 2018
in
Probability and Statistics
by
Milicevic3306
(
15.8k
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39
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gate2014ec3
probabilityandstatistics
probability
independentevents
randomvariable
uniformdistribution
numericalanswers
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13
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 ________.
asked
Mar 26, 2018
in
Probability and Statistics
by
Milicevic3306
(
15.8k
points)

27
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gate2014ec2
probabilityandstatistics
probability
uniformdistribution
randomvariable
numericalanswers
0
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14
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 ______.
asked
Mar 26, 2018
in
Probability and Statistics
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Milicevic3306
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15.8k
points)

35
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gate2014ec2
numericalanswers
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randomvariable
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15
GATE ECE 2014 Set 1  Question: 49
Let $X$ be a realvalued 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 $(E[X])^{2}>E[X^{2}]$ $E[X^{2}]\geq (E[X])^{2}$ $E[X^{2}] = (E[X])^{2}$ $E[X^{2}] > (E[X])^{2}$
asked
Mar 26, 2018
in
Probability and Statistics
by
Milicevic3306
(
15.8k
points)

28
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gate2014ec1
probabilityandstatistics
probability
randomvariable
expectation
0
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0
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16
GATE ECE 2013  Question: 38
Consider two identically distributed zeromean 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 $x$ $F(x)  G(x) \leq 0$ $F(x)  G(x) \geq 0$ $(F(x)  G(x)) \cdot x\leq 0$ $(F(x)  G(x)) \cdot x\geq 0$
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Mar 26, 2018
in
Probability and Statistics
by
Milicevic3306
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15.8k
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62
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gate2013ec
probabilityandstatistics
probability
randomvariable
0
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0
answers
17
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 $4/9$ $1/2$ $2/3$ $5/9$
asked
Mar 26, 2018
in
Probability and Statistics
by
Milicevic3306
(
15.8k
points)

32
views
gate2013ec
probabilityandstatistics
probability
randomvariable
independentevents
0
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0
answers
18
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 $\frac{3}{4}$ $\frac{9}{16}$ $\frac{1}{4}$ $\frac{2}{3}$
asked
Mar 25, 2018
in
Probability and Statistics
by
Milicevic3306
(
15.8k
points)

35
views
gate2012ec
probabilityandstatistics
probability
independentevents
randomvariable
0
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0
answers
19
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 ________.
asked
Feb 19, 2018
in
Probability and Statistics
by
gatecse
(
1.5k
points)

55
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gate2018ec
numericalanswers
probabilityandstatistics
propability
randomvariable
0
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0
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20
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 ________.
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Feb 19, 2018
in
Probability and Statistics
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gatecse
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1.5k
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62
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gate2018ec
numericalanswers
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randomvariable
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21
GATE ECE 2017 Set 2  Question: 22
Consider the random process $X(t)=U+Vt,$ Where $U$ is a zeromean 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 ________
asked
Nov 23, 2017
in
Probability and Statistics
by
admin
(
2.8k
points)

51
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gate2017ec2
numericalanswers
probabilityandstatistics
probability
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