answer all questions with explanation

1.2 (a) [1.5 marks} Suppose a random variable X has pdf f($) = 2:1:8' , where a: > 0. Draw a random sample of size 100 from this distribution. Draw a histogram of the 100 sampled values and obtain the sample mean and standard deviation. (b) [1.5 marks} Using your sample obtained above, draw a histogram and calculate mean and variance for 100 sampled values for the random variable Y = X 2. (c) [2 marks] From the pdf f(x) = 2:3632, where .r > 0, nd the distribution of Y = X 2. The distribution of Y is a special case of which distribution? Hence, what are E (Y) and Var(Y)