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Show transcribed image text Example 1 Let X1 ~ bin(n1, p) and X2 ~ bin(n2, p) (with the same parameter p), which are independent. Then, X1 + X2 ~ bin(n1 + n2, p) (using two methods: (a) the direct method, and (b) the MGF method): P = (X1 = k|X1 + X2 = m) ~ hypergeometric, or P = (X1 = k|X1 + X2 = m) = .
Example 1 Let X1 ~ bin(n1, p) and X2 ~ bin(n2, p) (with the same parameter p), which are independent. Then, X1 + X2 ~ bin(n1 + n2, p) (using two methods: (a) the direct method, and (b) the MGF method): P = (X1 = k|X1 + X2 = m) ~ hypergeometric, or P = (X1 = k|X1 + X2 = m) = .
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