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Mr and Mrs Brown decide to continue having children until they either have their ﬁrst boy or until they have

ﬁve children. Assume that each child is equally likely to be a boy or a girl, independent of all other children,

and that there are no multiple births. Let B and G denote the numbers of boys and girls respectively that the

Browns have.

(a) Write down the sample space together with the probability of each sample point.

Sample Space with probability = {B 1/2, GB 1/4, GGB 1/8, GGGB, 1/16, GGGGB 1/32, GGGGG 1/32}

(b) Write down the distributions of the random variables B and G.

Pr[B=0] = 1/32, Pr[B=1] = 31/32

Pr[G=0] = 1/2, Pr[G=1] = 1/4, Pr[G=2] = 1/8, Pr[G=3] = 1/16, Pr[G=4] = 1/32, Pr[G=5] = 1/32,

(c) Compute the expectations of B and G using a direct calculation

E(B) = 31/32

Is this below part correct. For some reason I don't think it could be correct.

E(G) = 31/32??????