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

  • $\begingroup$ "Correlated" is not synonymous with "not independent". Which one do you want to know about? $\endgroup$ – Chris Eagle May 30 '12 at 18:26
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    $\begingroup$ @ChrisEagle for jointly normal random variables, being uncorrelated is equivalent to independence. He has to mean that these two random variables are jointly normal, or else this question doesn't have an answer. $\endgroup$ – Chris Janjigian May 30 '12 at 18:38

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


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