1
GATE EE 2025
MCQ (Single Correct Answer)
+2
-0.67

Let $X$ and $Y$ be continuous random variables with probability density functions $P_X(x)$ and $P_Y(y)$, respectively. Further, let $Y=X^2$ and $P_X(x)=\left\{\begin{array}{cc}1, & x \in(0,1] \\ 0, & \text { otherwise }\end{array}\right.$.

Which one of the following options is correct?

A
$P_Y(y)=\left\{\begin{array}{cc}\frac{1}{2 \sqrt{y}}, & y \in(0,1] \\ 0, & \text { otherwise }\end{array}\right.$
B
$P_Y(y)=\left\{\begin{array}{lc}1, & y \in(0,1] \\ 0, & \text { otherwise }\end{array}\right.$
C
$P_Y(y)=\left\{\begin{array}{cc}1.5 \sqrt{y}, & y \in(0,1] \\ 0, & \text { otherwise }\end{array}\right.$
D
$P_Y(y)=\left\{\begin{array}{cc}2 y, & y \in(0,1] \\ 0, & \text { otherwise }\end{array}\right.$
2
GATE EE 2023
Numerical
+2
-0

The expected number of trials for first occurrence of a "head" in a biased coin is known to be 4. The probability of first occurrence of a "head" in the second trial is __________ (Round off to 3 decimal places).

Your input ____
3
GATE EE 2022
Numerical
+2
-0

Let the probability density function of a random variable x be given as

f(x) = ae$$-$$2|x|

The value of a is _________.

Your input ____
4
GATE EE 2017 Set 2
MCQ (Single Correct Answer)
+2
-0.6
A person decides to toss a fair coin repeatedly until he gets a head. He will make at most $$3$$ tosses. Let the random variable $$Y$$ denotes the number of heads. The value of var $$\left\{ Y \right\},$$ where var $$\left\{ . \right\}$$ denotes the variance, equal
A
$${7 \over 8}$$
B
$${49 \over 64}$$
C
$${7 \over 64}$$
D
$${105 \over 64}$$
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