a) and b) please

1 Let X1, . . ., Xn be a sample from U(0, 0). a) If n is an odd integer, find the density of the median of the sample. b) Show that the median of the sample converges to the median of the population in proba- bility as n - co. Hint: The beta density is given by r(a + B) f(I) = T(a )T(B) 2"-1(1 -2)-1, 0 0, B>0. Mean= "and variance= (atB )-(atB+1 ). (10 pts)