Please help.

Let X be a positive continuous random variable with the PDF 20 points f(x)= J 2/1: exp(- x212), x>0 It can be shown that E(X) = Z, E(X2) =1, so you do not need to verify. a. Let Y=g(X)=)(2 and use the method of transformation to verify that Y has a gamma distribution. Identify the parameters of the gamma distribution. b. Use part (a) and Taylor series expansion order 3 about the mean of Y to approximate E[e"Y']. Hint: You can use the following result: If W -- Gamma (a,B) then E[W"]= 3mm\". 1:- > 0. You may use software to compute rm) Gamma functions. 0. Let X1....,Xn be a random sample from the above pdf. Determine the value of 1 E": x2 constant It so that 9;; rk in probability, where s is the sample standard deviation