0
$\begingroup$

Let there be 3 normal distributions $X\sim\mathcal{N}(\mu_x,\sigma_x)$, $Y\sim\mathcal{N}(\mu_y,\sigma_y)$, $Z\sim\mathcal{N}(\mu_z,\sigma_z)$ and 3 random samples from each distribution- $x,y,z$. how can I find the probability of $P(x>y\textrm{ and } x>z)$. That is, the probability that the sample $x$ will be larger both from the sample $y$ and from the sample $z$. (assuming the distributions are independent)

Thanks for the help!

$\endgroup$
0
$\begingroup$

In general it involves the integration of multivariate normal pdf (as they are independent and thus they jointly follow a multivariate normal), which has no closed form available, unless the mean is zero.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.