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user158675
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Can someone help me on this question? I'm finding a very strange probability distribution.
Question: Suppose that x_1 and x_2 are independent with x_1 ~ geometric(p) and x_2 ~ geometric (1-p). That's x_1 has geometric distribution with parameter p and x_2 has geometric distribution with parameter 1-p.
Find the distribution of P(x_1 = k| x_1 + x_2 = n)
I found P^-k (1-p)^k-1(2p-1)/1-(1-p)^n-1, but that's certainly wrong.
Question: Suppose that x_1 and x_2 are independent with x_1 ~ geometric(p) and x_2 ~ geometric (1-p). That's x_1 has geometric distribution with parameter p and x_2 has geometric distribution with parameter 1-p.
Find the distribution of P(x_1 = k| x_1 + x_2 = n)
I found P^-k (1-p)^k-1(2p-1)/1-(1-p)^n-1, but that's certainly wrong.