Probability that one normal distribution is greater than the other when they are correlated i.e (Not Independent)

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Would like to know how to approach this question: Probability that one normal distribution is greater than the other when they are correlated i.e (Not Independent).

Seen the solution for the independent normal distributions already. Thanks

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Hint: Assuming $X$ and $Y$ are jointly normal random variables, $W = X - Y$ is normal. What are its mean and variance? You want $P(W > 0)$.