Thanks for your help. I was really stuck on the wording of the question and I'm still a bit lost on what I'm sort of meant to do.

You started with a random variable \(X\). You were given the CDF of \(X\).

You then pull out a

**new** random variable \(Y\). You are told that this new random variable is

**related** to the old one, by the equation \( Y = \sqrt{X}\). (So you see that \(Y\) is in fact a

**function** of another random variable, and hence also a random variable.)

Since \(Y\) is a new random variable, it should

**also** have a CDF. You are asked to find this CDF in the first part. (And then using it, you can find the PDF in the second part.)

(But how would you be able to find the CDF of \(Y\) to begin with? Well, you're given the relationship \( Y = \sqrt{X}\), and the CDF of \(X\). So somehow you had to puzzle the two together.)

The actual technique used is understandably one you might've not seen before. But as for what the question was asking, you needed to realise most of the above.