Please provide detailed, neat, and clear solutions step by step for the entire problem (a-c)? Thanks!

6. Let X1, X2 is a random sample of size 2 from a distribution having pdf f(x, 0) = (1/0)e-z/, with x > 0,0 > 0, zero elsewhere. (a) Show that Y1 = X1 + X2 is a sufficient statistic for 0. Name: Score: HW04-SP2022-Math-440A (b) Let Y2 = X2. Show that Yz is an unbiased estimator of ( with variance (". (c) Find E()|Y1 = vi) = E(Yelvi) = () and the variance of o( Y1 )