Let X be a random variable with the probability density function fX(x)=begincases1/2,&0<x<1,1/4,&1<x<3,0,&otherwise.endcases If Y=X^2 and Z=1/X, then which of the following statements is/are true?

Q35Section B (Section B)35 of 60

Square and reciprocal transformations

Let $X$ be a random variable with the probability density function $f_{X}(x)=\begin{cases}\frac{1}{2},&0<x<1,\\\frac{1}{4},&1<x<3,\\0,&\text{otherwise.}\end{cases}$ If $Y=X^{2}$ and $Z=\dfrac{1}{X}$ , then which of the following statements is/are true?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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