Starting at a fixed time, we observe the gender of each newborn child at a certa

Question

Starting at a fixed time, we observe the gender of each newborn child at a certain hospital until a boy B X by X = number of births observed. Then is born. Let p P(B), assume that successive birth5 are independent, and define the and Continuing in this way, a general formula emerges p(x)-:(1-p)"-lp x= 1, 2, 3, otherwise and The expresslon above describes the family of geometric distributions. In the gender example, p -0.51 The parameter p can assume any value between might be appropriate, but if we were looking for the first child with Rh-positive blood, then we might have p 0.85.

Explanation / Answer

P(X=1) = P(B) = p
P(X=2) = P(GB) = P(G)P(B) = q p
P(X=3) = P(G)P(G)P(B) = q.q.p = q^2 p

The parameter p can assume any values between 0 and 1

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