Please help with this homework question and explain please.

True/False questions.

(a) If X is a normal random variable with mean 3 and variance 4, then 2X 6 is also a normal random variable with mean 0 and variance 8.

(b) Suppose that random variable X has mean 2 and variance 3, and random variable Y has mean 1 and variance 1. Then Z=2X+3Y 5 has mean 2 and variance 21.

(c) Given three random variables X, Y , Z, if X and Y are independent, X and Z are independent, then Y and Z are also independent.

(d) Let X be a continuous random variable with possible values in [0, 1]. Let Y be another continuous random variable with possible values in [0, 2]. Then Y must have a larger variance than X .

(e) In order to model a proportion, it is a good choice to use gamma distributions.