2. (a) Let mean is 2 then use the poisson distribution for find the P(X ≤ 4), P(X ≥ 5) and P(X=3). and also find moment generating function M_X=3(t = 3) for same given problem.
(b) X: -2, -1, 0, 1, 2, 3 p(x): 0.1, k, 0.2, 2k, 0.3, k (1) Find the value of k, mean and variance. (2). Construct CDF and drar the graph.
3.(a)X: -0, -1, 2, 3
p(x): 0.1, 0.3, 0.5, 0.1
Find probability function of Y=X^2+2X . Also find P(X ≤ 3), P(1 < X ≤ 3) and P(X = 3). (b) f(x)=cx^2(1 − x), 0 < x < 1 then find the constant c, P(−1 < X < 0.5), P(0.2 < X < 0.8).
