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Mahler Exam #4 Q12
1. I am trying to solve Mahler's Exam 4 Q12 using conjugate prior:
The number of boys in a family with m children is Binomial. The parameter q varies between different families with Beta distribution where a=3, b=1, Θ=1. What is the probability that a family with 6 children have 5 boys and 1 girl. 2. From the C table, Distribution for Beta is given as F(x) = Beta(a, b; u). Can one evaluate F(x) without integrating? If yes how? 3. Is there any relationship between Beta and another distribution when a=b? Thanks.
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The key to this problem is that Θ=1. Once you know this, the problem simplifies to (you can plug it into the distribution to find it out for yourself):
Γ(a+b)/Γ(a)Γ(b) x^(a1) (1x)^(b1) I found that they may also put the distribution in this form and you need identify a, b, and Θ from this. Hope this helps!
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