ow that if U and degrees of freedom respectively, then are independent random variables having chỉ- X = a random variable having an F distribution with v and v2 deg riable whose probability density function is given by (2) f (2) 17-1 (1+ I (4)r()

Two discrete random variables X and Y have joint probability mass function (pmf) (a) (b) (c) ƒ(x) = { 5 0 Calculate the value of k. Show that f(x|y) Show that f(y x) = k n(n+1) = 1 n 1 8 x = 1,2,..., n; y=1,2,...,x. otherwise

and variance of X if the probability mass function is f(x) = ; ;)" , Find the moment generating function, mean x = 1, 2, 3, 4, ...

9/10 Question * If the probability density function of random variable X is given by: - 1)(2- x), 0, 15 xS 2; otherwise. The value of k is equal to: None of these 3/2 7. 6. Question *