Probability & Statistics Ch.2 Section 1 Question 14

Solutions for “Probability and Statistics: The Science of Uncertainty” (Second Edition). These are solutions I have come up with; I offer no guarantee of accuracy.

Question

Suppose X is a random variable. Let $Y=\sqrt{X}$. Must Y be a random variable? Explain.

Solution

Yes, Y must be a random variable as its value is dependent on the value of another random variable X.

(Note: Y is only defined when X takes non-negative values, but where it is defined, it remains a random variable.)