Math Is Fun Forum

freddogtgj

Member

Registered: 2006-12-02

Posts: 54

Stats Help Needed!

Consider the birth of twins. Let Φ denote the probability that they are identical, in
which case they must be of the same gender. If they are fraternal, that is, not identical
twins, each child is equally likely to be male or female independently of the other child.

(a) Justify the result that
P(twins are of the same gender) =

(b) Let Y be the number of pairs of twins of the same gender out of m pairs of twins.
Then Y has a binomial distribution with parameters m and (1+Φ)/2. Write down the
likelihood for the single observation y of Y .

Thanks in advance!

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Stats Help Needed!

a)

probability of them not being identical is (1-Φ), for this there are 4 outcomes: M+F, M+M, F+F, F+M. two of which give that they are the same gender, so the probability that they are the same gender is ½ given that they are fraternal, hence the probablity that they are fraternal and of the same gender is ½(1-Φ). probability that they are identical is Φ, and given this, probabilty of being same gender is 1. adding them together you get Φ+½(1-Φ) = ½(1+2Φ-Φ) = ½(1+Φ)

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