Pillai_'Var(X+Y): Variance of the Sum of Two Random Variables'

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Classic problem on finding the variance of the sum of two random variables both in the correlated and the uncorrelated cases. When the two random variables are uncorrelated, the variance of their sum/difference is shown to be the sum of their variances.
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Автор

what happens if condition is correlated? such as: Suppose that X ∼ N (µx, σ2x) and Y ∼ N (µy, σ2y) are continuous random variables that are correlated (i.e., E[XY] = σxy is not equal to 0). We can define a third random variable as the sum of the first two:
Z = αX + βY. What is the expected value µz and variance σ^2_z? Express your answers in terms of the variables µx, µy, σx, σy, σxy.

dewanmohammedabdulahad
Автор

good job prof. you did a very good proof

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