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Recent questions tagged probabilityandstatistics
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GATE2020EC: 54
$X$ is a random variable with uniform probability density function in the interval $[2,\:10]$. For $Y=2X6$, the conditional probability $P\left ( Y\leq 7\mid X\geq 5 \right )$ (rounded off to three decimal places) is __________.
asked
Feb 13
in
Probability and Statistics
by
jothee
(
1.4k
points)
gate2020ec
numericalanswers
probabilityandstatistics
0
votes
0
answers
2
GATE201612
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
(
15.8k
points)
gate2016ec1
numericalanswers
probabilityandstatistics
engineeringmathematics
0
votes
0
answers
3
GATE201441
The series $\Sigma_{n=0}^{\infty} \frac{1}{n!}$ converges to $2 \text{ ln } 2$ $\sqrt{2}$ $2$ $e$
asked
Mar 26, 2018
in
Probability and Statistics
by
Milicevic3306
(
15.8k
points)
gate2014ec4
probabilityandstatistics
engineeringmathematics
0
votes
0
answers
4
GATE2014249
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
by
Milicevic3306
(
15.8k
points)
gate2014ec2
numericalanswers
probabilityandstatistics
engineeringmathematics
+1
vote
1
answer
5
GATE201412
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 ________.
asked
Mar 26, 2018
in
Probability and Statistics
by
Milicevic3306
(
15.8k
points)
gate2014ec1
numericalanswers
probabilityandstatistics
engineeringmathematics
0
votes
0
answers
6
GATE201415
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 ________.
asked
Mar 26, 2018
in
Probability and Statistics
by
Milicevic3306
(
15.8k
points)
gate2014ec1
numericalanswers
probabilityandstatistics
engineeringmathematics
0
votes
0
answers
7
GATE2014123
The capacity of a Binary Symmetric Channel $\text{(BSC)}$ with crossover probability $0.5$ is ________.
asked
Mar 26, 2018
in
Probability and Statistics
by
Milicevic3306
(
15.8k
points)
gate2014ec1
numericalanswers
probabilityandstatistics
engineeringmathematics
0
votes
0
answers
8
GATE2014149
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)
gate2014ec1
probabilityandstatistics
engineeringmathematics
0
votes
0
answers
9
GATE2014150
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 autocorrelation $E[X(t_{1})X(t_{2})]$ is $\cos(2\pi(t_{1} + t_{2}))$ $\sin(2\pi(t_{1}  t_{2}))$ $\sin(2\pi(t_{1} + t_{2}))$ $\cos(2\pi(t_{1}  t_{2}))$
asked
Mar 26, 2018
in
Probability and Statistics
by
Milicevic3306
(
15.8k
points)
gate2014ec1
probabilityandstatistics
correlationandregressionanalysis
0
votes
0
answers
10
GATE201338
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 $x$ $F(x)  G(x) \leq 0$ $F(x)  G(x) \geq 0$ $(F(x)  G(x)) \cdot x\leq 0$ $(F(x)  G(x)) \cdot x\geq 0$
asked
Mar 26, 2018
in
Probability and Statistics
by
Milicevic3306
(
15.8k
points)
gate2013ec
probability
probabilityandstatistics
engineeringmathematics
0
votes
0
answers
11
GATE201326
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)
gate2013ec
probabilityandstatistics
probability
engineeringmathematics
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