answer with detailed explanation

(c) Consider the inverse Gaussian random variable Y with pdf B f(y) = 2my3 e - zy (414 )2 , y > 0, where B > 0 and > > 0 are parameters. You are given: . The kth moment of Y is E(YK) = ( k t n - 1)! Anth (k - n - 1)!n! (23)> > k = 1, 2, .... n= . The modified Bessel function, K,(y) may be define, for half integer values of the index parameter A, by K_,(y) = Ky(y), together u (u + j)! Kutt (y) = 1 2y (u - j)!j! , u = 0, 1, .... 1=0 2y Prove that, for E > 0, B > 0, and u = 0, 1, . .., yu -le-e- fudy = 2 26 Ku- V2EB)