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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 $\sigma ^{2}_{Y}=2 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=4 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=5 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=25 \sigma ^{2}_{X}$
Arjun
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in
Probability and Statistics
Feb 20
by
Arjun
4.5k
points
50
views
gateec-2021
probability-and-statistics
random-variable
variance
0
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0
answers
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 ___________.
jothee
asked
in
Probability and Statistics
Feb 13, 2020
by
jothee
1.9k
points
106
views
gate2020-ec
numerical-answers
probability-and-statistics
probability
independent-events
random-variable
expectation
0
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0
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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 $E\left[X\right]+E\left[Y\right]=$___________.
Arjun
asked
in
Probability and Statistics
Feb 12, 2019
by
Arjun
4.5k
points
63
views
gate2019-ec
numerical-answers
probability-and-statistics
probability
random-variable
expectation
0
votes
0
answers
4
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 ___________.
Arjun
asked
in
Probability and Statistics
Feb 12, 2019
by
Arjun
4.5k
points
146
views
gate2019-ec
numerical-answers
probability-and-statistics
probability
random-variable
0
votes
0
answers
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 _________.
Arjun
asked
in
Probability and Statistics
Feb 12, 2019
by
Arjun
4.5k
points
97
views
gate2019-ec
numerical-answers
probability-and-statistics
probability
random-variable
uniform-distribution
0
votes
0
answers
6
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 _____
Milicevic3306
asked
in
Probability and Statistics
Mar 28, 2018
by
Milicevic3306
15.8k
points
31
views
gate2016-ec-1
numerical-answers
probability-and-statistics
probability
poisson-distribution
random-variable
0
votes
0
answers
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 __________.
Milicevic3306
asked
in
Probability and Statistics
Mar 28, 2018
by
Milicevic3306
15.8k
points
55
views
gate2015-ec-3
numerical-answers
probability-and-statistics
propability
random-variable
variance
0
votes
0
answers
8
GATE ECE 2015 Set 3 | Question: 52
A random binary wave $y(t)$ is given by $y(t) = \sum_{n = -\infty}^{\infty}X_{n}\:p(t-nT-\phi)$ 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 _________.
Milicevic3306
asked
in
Probability and Statistics
Mar 28, 2018
by
Milicevic3306
15.8k
points
34
views
gate2015-ec-3
numerical-answers
probability-and-statistics
probability
random-variable
uniform-distribution
0
votes
0
answers
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 _______.
Milicevic3306
asked
in
Probability and Statistics
Mar 28, 2018
by
Milicevic3306
15.8k
points
23
views
gate2015-ec-2
numerical-answers
probability-and-statistics
probability
random-variable
expectation
0
votes
0
answers
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 $pq+(1-p)(1-q)$ $pq$ $p(1-q)$ $1-pq$
Milicevic3306
asked
in
Probability and Statistics
Mar 28, 2018
by
Milicevic3306
15.8k
points
24
views
gate2015-ec-2
probability-and-statistics
probability
random-variable
0
votes
0
answers
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 __________
Milicevic3306
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in
Vector Analysis
Mar 26, 2018
by
Milicevic3306
15.8k
points
33
views
gate2014-ec-4
numerical-answers
vector-analysis
gausss-theorem
random-variable
0
votes
0
answers
12
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 _________.
Milicevic3306
asked
in
Probability and Statistics
Mar 26, 2018
by
Milicevic3306
15.8k
points
49
views
gate2014-ec-3
probability-and-statistics
probability
independent-events
random-variable
uniform-distribution
numerical-answers
0
votes
0
answers
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 ________.
Milicevic3306
asked
in
Probability and Statistics
Mar 26, 2018
by
Milicevic3306
15.8k
points
31
views
gate2014-ec-2
probability-and-statistics
probability
uniform-distribution
random-variable
numerical-answers
0
votes
0
answers
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 ______.
Milicevic3306
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Probability and Statistics
Mar 26, 2018
by
Milicevic3306
15.8k
points
39
views
gate2014-ec-2
numerical-answers
probability-and-statistics
probability
probability-density-function
random-variable
0
votes
0
answers
15
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 $(E[X])^{2}>E[X^{2}]$ $E[X^{2}]\geq (E[X])^{2}$ $E[X^{2}] = (E[X])^{2}$ $E[X^{2}] > (E[X])^{2}$
Milicevic3306
asked
in
Probability and Statistics
Mar 26, 2018
by
Milicevic3306
15.8k
points
33
views
gate2014-ec-1
probability-and-statistics
probability
random-variable
expectation
0
votes
0
answers
16
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 $x$ $F(x) - G(x) \leq 0$ $F(x) - G(x) \geq 0$ $(F(x) - G(x)) \cdot x\leq 0$ $(F(x) - G(x)) \cdot x\geq 0$
Milicevic3306
asked
in
Probability and Statistics
Mar 26, 2018
by
Milicevic3306
15.8k
points
78
views
gate2013-ec
probability-and-statistics
probability
random-variable
0
votes
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 $4/9$ $1/2$ $2/3$ $5/9$
Milicevic3306
asked
in
Probability and Statistics
Mar 26, 2018
by
Milicevic3306
15.8k
points
46
views
gate2013-ec
probability-and-statistics
probability
random-variable
independent-events
0
votes
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 $\frac{3}{4}$ $\frac{9}{16}$ $\frac{1}{4}$ $\frac{2}{3}$
Milicevic3306
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in
Probability and Statistics
Mar 25, 2018
by
Milicevic3306
15.8k
points
39
views
gate2012-ec
probability-and-statistics
probability
independent-events
random-variable
0
votes
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 ________.
gatecse
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in
Probability and Statistics
Feb 19, 2018
by
gatecse
1.5k
points
65
views
gate2018-ec
numerical-answers
probability-and-statistics
propability
random-variable
0
votes
0
answers
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 ________.
gatecse
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in
Probability and Statistics
Feb 19, 2018
by
gatecse
1.5k
points
74
views
gate2018-ec
numerical-answers
probability-and-statistics
probability
random-variable
variance
0
votes
0
answers
21
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 ________
admin
asked
in
Probability and Statistics
Nov 23, 2017
by
admin
2.8k
points
58
views
gate2017-ec-2
numerical-answers
probability-and-statistics
probability
random-variable
uniform-distribution
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