Question

2(15)(a) An urn contains 4 white and 4 black balls. We randomly choose 4 balls. If 2 of them are white and 2 are black, we stop. If not, we replace the balls in the urn and again randomly select 4 balls. This continues until exactly 2 of the 4 chosen are white. What is the probability that we shall maken selections? (b)Compute E[x2] for a Poisson random variable X.

Answer 1

(a) our success if we get & white and 2 Black balls - out of h chosen balls from & balls. 6x6x4x3x4 5x7x6x5 . Probability of success = 4 x 2 (b) Q þ= 19 so q = 115 35 This question u of Negative Binomial distribution and a special case is Geometric distribution- Since the quation ask for the probability that we make a selection so it means that till n-1 trials we get failure and at nth trial we get success. . selections probability that we make a = g h l , n= 1, 2, -

XN pla) so fra) - ceny*, 2-0,1,2, A 30 xl A n=1 (2-1)! 7 x=2 (2-2)! aperted to dete = + = alatio inwer-