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Electrical and Electronic EngineeringEngineering MathematicsMultiple Choice (MCQ)2 Marks

Q3.

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

$P_X(x) = \begin{cases} 1, & x \in (0,1] \\ 0, & \text{otherwise} \end{cases}$

Which one of the following options is correct?

A

P_Y(y) = \begin{cases} \frac{1}{2\sqrt{y}}, & y \in (0,1] \\ 0, & \text{otherwise} \end{cases}

B

P_Y(y) = \begin{cases} 1, & y \in (0,1] \\ 0, & \text{otherwise} \end{cases}

C

P_Y(y) = \begin{cases} 1.5\sqrt{y}, & y \in (0,1] \\ 0, & \text{otherwise} \end{cases}

D

P_Y(y) = \begin{cases} 2y, & y \in (0,1] \\ 0, & \text{otherwise} \end{cases}

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