Please answer the following question. Don't copy others answers, thank you!

J lIIIIueIz-iti-an 3 [2|] marks} Assume Z]... 32. .... is a. Sequence of 11:1 rvs an that Erika} = EM]. + 51}, for j E N. {:1} Determine the law of U where U ;= Z 33-21. {6 marks} j=1 {b} Determine the expected value and variance of C where C := 222331. {3 marks} i=1 (c) Assume Yi, Y2, . .. is a sequence of iid rvs so that C(Y;) = 160 + $61, for je N. Show that the laws of C and W are singular where 00 W := 2)Y, 3 . (6 marks) j=1