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Joint probability distribution of several random variables gives the probability that all of them simultaneously lie in a particular region.
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trivariate normal distribution and joint distribution
Suppose that r.v $X$ and $Y$ are normally distributed and independent each other. Under which conditions $(X,Y)$ are bivariate normally distributed?
Now I want to calculate $\text{Prob}(X>a, Y<a, bX+c …
4
votes
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Multivariate normal distribution
I have 4 r.v $(X,Y,W,Z)$ distributed as a multivariate normal.
Mean and variance-covariance matrix are known.
Is it possible to calculate, for example
$\mathrm{Prob} (aX+bY < k, W >0,Z >0, W-Z >0) …