(a) [1.5 marks) Suppose a random variable X has pdf f(x) = 2xe-r?, where x > 0. Draw a random sample of size 100 from th

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A 1 5 Marks Suppose A Random Variable X Has Pdf F X 2xe R Where X 0 Draw A Random Sample Of Size 100 From Th 1 (64.5 KiB) Viewed 90 times

(a) [1.5 marks) Suppose a random variable X has pdf f(x) = 2xe-r?, where x > 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?. (c) [2 marks] From the pdf f(x) 2xe-r2, where I > 0, find the distribution of Y = X?. The distribution of Y is a special case of which distribution? Hence, what are E(Y) and Var(Y)?