Let X and Y be two random variables such that X + Y = 100. If X follows Binomial distribution with parameters n = 100 and p = 4/5, what is the variance of Y? 1. 1 2. 1/2 3. 16 4. 1/16
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If \( Y = 100 - X \), then: \[ \text{Var}(Y) = \text{Var}(100 - X) \] Step 6: Since the variance of a constant is zero and the variance of \( -X \) is the same as the variance of \( X \): \[ \text{Var}(Y) = \text{Var}(100) + \text{Var}(-X) \] \[ \text{Var}(Y) = 0 Show more…
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