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Joint probability distribution of several random variables gives the probability that all of them simultaneously lie in a particular region.

1 vote
1 answer
2k views

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 …
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  • 437
4 votes
1 answer
406 views

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) …
Andrea's user avatar
  • 437