Let ? h? ave the Pareto pdf introduced in Exercise 10. a.? f k>1, compute E ? ?(? . b.? ?What can you say about ?E?(?X?) if k=1? c.? ?If k>2 , show thatV(X) = k?2 (k – 1)– 2(k –2)–1. d.? ?If k=2, what can you say about V ? ?(?X?)? e.? hat conditions on ?k ?are necessary to ensure that E(Xn) is finite?

Solution : Step 1: It is given the random variable X ~ pareto distribution with pdf Step 2: a) We have to find the E(x) , when K>1 E(x) = x f(x) dx K K = x xK+1 dx K X = k XK+1 dx = k [X-k/ -k+1] = k [0 - (K+1/ K + 1)] , when K>1. K = K1 b) We have to find E(x) when K=1 It will be E(x) = K K1 = (undefined)