Extra credit Due: 12/11/2015 Each part is worth .5 extra credit toward your nal course grade. This means that one could get a maximum of 4 extra points added to their nal course grade. Each part is worth all or nothing. You may do as many parts as you would like to submit. The same guidelines that apply to homework format apply to the extra credit assignment 1. Let X, Y have the joint pdf: f (x, y) = 2 1 1 (2y) 2 e ( x +y) 2y if < x < , 0 < y 0 else a) Derive the marginal density fY (y) of Y b) Derive the moment generating function mX (t) of X 2. Let Xi N (, 2 ) for i = i, 2, ..., n and let X1 , X2 , ..., Xn be mutually independent. Dene Yi , for i = 1, 2, ..., n to be: Yi = 1 if 0 if Xi Xi < a) Derive the distribution of Yi for i = 1, 2, ..., n b) Derive the distribution of n i=1 Yi 3. Let X have the pdf: f (x) = 2xe2x + cx2 e3x if 0 a) Find the value of c b) Find the mean of X 1 0