Let Y1, Y2, ..., Yn be a random sample of size n from the pdf

f_Y(y;theta) = (1/((r-1)!*theta^r))*y^(r-1)*e^(-y/theta), y>0, and r>0 is unknown.

a) Show that theta hat = (1/r)*Ybar is an unbiased estimator for theta.

b) Show that theta hat =(1/r)*Ybar is a minimum variance estimator for theta.

c) Find a sufficient statistic for theta.

Thanks in advance for any help.