Question

2. Suppose that a family is going to keep having children until they have at least one girl. Further suppose we can model successive births as boy and one independent trials with p P(girl) and P(boy) = 1 - p. Let Y denote the total number of children in the family. Compute, for y 2, (i) the probability that the first boy born is the y-th child born; [2] (ii the probability that the first girl born is the y-th child born; [2] (iii P(Y y) 2] (iv) E(Y). [4

Answer 1

Pi) PIboy ичы beh of childten in the fimnily. ttal У! и Bao bodn ithe -chd.hom (1-) * и иy 12в гg pog heingog«{ a ychild Р(r) +l-) (()(k) iv)ElY) 4.(4-0) + (4-1). д-2