1
GATE EE 2025
MCQ (Single Correct Answer)
+1
-0.33

Consider discrete random variable $X$ and $Y$ with probabilities as follows:

$$ \begin{aligned} & P(X=0 \text { and } Y=0)=\frac{1}{4} \\ & P(X=1 \text { and } Y=1)=\frac{1}{8} \\ & P(X=0 \text { and } Y=1)=\frac{1}{2} \\ & P(X=1 \text { and } Y=1)=\frac{1}{8} \end{aligned} $$

Given $X=1$, the expected value of $Y$ is

A
$\frac{1}{4}$
B
$\frac{1}{2}$
C
$\frac{1}{8}$
D
$\frac{1}{3}$
2
GATE EE 2024
MCQ (More than One Correct Answer)
+1
-0

Let $X$ be a discrete random variable that is uniformly distributed over the set {$-10, -9, \cdots, 0, \cdots, 9, 10$}. Which of the following random variables is/are uniformly distributed?

A

$X^2$

B

$X^3$

C

$(X - 5)^2$

D

$(X + 10)^2$

3
GATE EE 2017 Set 2
MCQ (Single Correct Answer)
+1
-0.3
An urn contains $$5$$ red balls and $$5$$ black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a red ball in the second draw is
A
$${1 \over 2}$$
B
$${4 \over 9}$$
C
$${5 \over 9}$$
D
$${6 \over 9}$$
4
GATE EE 2017 Set 2
Numerical
+1
-0
Assume that in a traffic junction, the cycle of the traffic signal lights is $$2$$ minutes of green (vehicle does not stop) and $$3$$ minutes of red (vehicle stops). Consider that the arrival time of vehicles at the junction is uniformly distributed over $$5$$ minute cycle. The expected waiting time (in minutes) for the vehicle at the junction is _________.
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