The discussion focuses on solving binomial distribution problems involving conditional probabilities. Specifically, it addresses the computation of P(X=2, N=4), P(X=1), and P(N=4|X=1) given that X|N follows a binomial distribution with parameters (n, 1/2) and N is uniformly distributed over {2, 4, 6}. The correct calculation for P(X=2, N=4) is confirmed as 0.375. The next steps involve calculating P(X=1) by determining the probabilities for each value of N.
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Yes, that is correct.cse63146 said:Homework Statement
Suppose that the conditional distribution of X given that N = n is binomial (n, 1/2) and the distribution of N is uniform over {2,4,6}
a) Determine P(X=2, N = 4)
b) Determine P(X=1)
c) Determine P(N = 4| X =1)
Homework Equations
The Attempt at a Solution
the way I understood the question was that X|N~bin(n, 1/2)
for a) I did (4C2)(0.5)2(0.5)2 = 0.375
Since N is uniform on 2, 4, 6, find P(X|N=2), P(X|N= 4), and P(X|N= 6). P(N= 2)= P(N= 4)= P(N= 6)= 1/3.I'm stuck for b). Any hints?