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Recent questions tagged uniform-distribution
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TIFR ECE 2014 | Question: 1
Consider two independent and identically distributed random variables $X$ and $Y$ uniformly distributed in $[0,1]$. For $\alpha \in[0,1]$, the probability that $\alpha \max (X, Y)<\min (X, Y)$ is $1 /(2 \alpha)$. $\exp (1-\alpha)$ $1-\alpha$ $(1-\alpha)^{2}$ $1-\alpha^{2}$
admin
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Probability and Statistics
Dec 14, 2022
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admin
43.6k
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16
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tifr2014
probability-and-statistics
probability
uniform-distribution
1
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2
TIFR ECE 2012 | Question: 15
Consider a string of length $1 \mathrm{~m}$. Two points are chosen independently and uniformly random on it thereby dividing the string into three parts. What is the probability that the three parts can form the sides of a triangle? $1 / 4$ $1 / 3$ $1 / 2$ $2 / 3$ $3 / 4$
admin
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Probability and Statistics
Dec 8, 2022
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admin
43.6k
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14
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tifr2012
probability-and-statistics
probability
uniform-distribution
1
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3
TIFR ECE 2021 | Question: 9
A stick of length $1$ is broken at a point chosen uniformly at random. Which of the following is false? Twice the length of the smaller piece is greater than the length of the larger piece with positive probability. One half of the length of the ... . The product of the length of the smaller piece and the larger piece is greater than $1 / 4$ with positive probability.
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Probability and Statistics
Nov 30, 2022
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admin
43.6k
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11
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tifrece2021
probability-and-statistics
probability
uniform-distribution
1
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0
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4
TIFR ECE 2020 | Question: 10
Consider two independent random variables $\left(U_{1}, U_{2}\right)$ both are uniformly distributed between $[0,1]$. The conditional expectation \[E\left[\left(U_{1}+U_{2}\right) \mid \max \left(U_{1}, U_{2}\right) \geq 0.5\right]\] equals $7 / 6$ $8 / 7$ $6 / 7$ $1.1$ None of the above
admin
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Probability and Statistics
Nov 30, 2022
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admin
43.6k
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11
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tifrece2020
probability-and-statistics
probability
uniform-distribution
1
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0
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5
TIFR ECE 2020 | Question: 12
Consider a unit disc $D$. Let a point $x$ be chosen uniformly on $D$ and let the random distance to $x$ from the center of $D$ be $R$. Which of the following is $\text{TRUE?}$ $R^{2}$ is uniformly distributed in $[0,1]$ $\pi R^{2}$ is uniformly ... $[0,1]$ $2 \pi R^{2}$ is uniformly distributed in $[0,1]$ None of the above
admin
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Probability and Statistics
Nov 30, 2022
by
admin
43.6k
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6
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tifrece2020
probability-and-statistics
probability
uniform-distribution
1
vote
0
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6
TIFR ECE 2019 | Question: 14
Consider the circle of radius $1$ centred at the origin in two dimensions. Choose two points $x$ and $y$ independently at random so that both are uniformly distributed on the circle. Let the vectors joining the origin to $x$ and $y$ be $X$ and $Y$, respectively. Let $\theta$ be ... $\mathbf{E}\left[|x-y|^{2}\right]=\sqrt{3}$ $\mathbf{E}\left[|x-y|^{2}\right]=1$
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Probability and Statistics
Nov 30, 2022
by
admin
43.6k
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6
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tifrece2019
probability-and-statistics
probability
uniform-distribution
1
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0
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7
TIFR ECE 2018 | Question: 7
Let $X_{1}, X_{2}$ and $X_{3}$ be independent random variables with uniform distribution over $[0, \theta]$. Consider the following statements. $E\left[\max \left\{X_{1}, X_{2}, X_{3}\right\}\right]=\frac{3}{4} \theta$ ... $\text{(i)}$ Only $\text{(ii)}$ Only $\text{(iii)}$ Only $\text{(iv)}$ All of $\text{(i) - (iv)}$
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Probability and Statistics
Nov 29, 2022
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admin
43.6k
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15
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tifrece2018
probability-and-statistics
probability
uniform-distribution
1
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0
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8
TIFR ECE 2017 | Question: 11
Consider a unit length interval $[0,1]$ and choose a point $X$ on it with uniform distribution. Let $L_{1}=X$ and $L_{2}=1-X$ be the length of the two sub-intervals created by this point on the unit interval. Let $L=\max \left\{L_{1}, L_{2}\right\}$. Consider ... $\text{(ii)}$ Only $\text{(i)}$ and $\text{(iii)}$ Only $\text{(ii)}$ and $\text{(iv)}$ None of the above
admin
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Probability and Statistics
Nov 29, 2022
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admin
43.6k
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15
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tifrece2017
probability-and-statistics
probability
uniform-distribution
1
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0
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9
TIFR ECE 2016 | Question: 10
Let $U_{1}, U_{2}, U_{3}$ be independent random variables that are each uniformly distributed between zero and one. What is the probability that the second highest value amongst the three lies between $1 / 3$ and $2 / 3?$ $\frac{2}{9}$ $\frac{1}{27}$ $\frac{13}{27}$ $\frac{1}{3}$ $\frac{7}{18}$
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Probability and Statistics
Nov 29, 2022
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admin
43.6k
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12
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tifrece2016
probability-and-statistics
probability
uniform-distribution
0
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0
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10
GATE ECE 2020 | Question: 54
$X$ is a random variable with uniform probability density function in the interval $[-2,\:10]$. For $Y=2X-6$, the conditional probability $P\left ( Y\leq 7\mid X\geq 5 \right )$ (rounded off to three decimal places) is __________.
go_editor
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Probability and Statistics
Feb 13, 2020
by
go_editor
1.9k
points
89
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gate2020-ec
numerical-answers
probability-and-statistics
probability
probability-density-function
uniform-distribution
0
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0
answers
11
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
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Probability and Statistics
Feb 12, 2019
by
Arjun
6.0k
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134
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gate2019-ec
numerical-answers
probability-and-statistics
probability
random-variable
uniform-distribution
0
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0
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12
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
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Probability and Statistics
Mar 28, 2018
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Milicevic3306
15.8k
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68
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gate2015-ec-3
numerical-answers
probability-and-statistics
probability
random-variable
uniform-distribution
0
votes
0
answers
13
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
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Probability and Statistics
Mar 26, 2018
by
Milicevic3306
15.8k
points
77
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gate2014-ec-3
probability-and-statistics
probability
independent-events
random-variable
uniform-distribution
numerical-answers
0
votes
0
answers
14
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
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Probability and Statistics
Mar 26, 2018
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Milicevic3306
15.8k
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54
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gate2014-ec-2
probability-and-statistics
probability
uniform-distribution
random-variable
numerical-answers
0
votes
0
answers
15
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 ________.
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Probability and Statistics
Mar 26, 2018
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Milicevic3306
15.8k
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70
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gate2014-ec-1
numerical-answers
probability-and-statistics
probability
uniform-distribution
0
votes
0
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16
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 $\cos(2\pi(t_{1} + t_{2}))$ $\sin(2\pi(t_{1} - t_{2}))$ $\sin(2\pi(t_{1} + t_{2}))$ $\cos(2\pi(t_{1} - t_{2}))$
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Mar 26, 2018
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Milicevic3306
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57
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gate2014-ec-1
probability-and-statistics
statistics
uniform-distribution
correlation-and-regression-analysis
0
votes
0
answers
17
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 ________
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Probability and Statistics
Nov 23, 2017
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admin
43.6k
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78
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gate2017-ec-2
numerical-answers
probability-and-statistics
probability
random-variable
uniform-distribution
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