Thread: bi-variate normal?

Hi
I am trying to find the probability of two events from two correlated normally distributed rv's. Would this be bi-variate normal and if so how would I go about calculating the probability?

Here's an example of what I'm trying to do,

Let's say I know peoples height (X) is normally distributed around some mean => I can calculate the probability someone is, say, at least 6ft tall.

Similarly say weight is normally distributed, and I can find the probability someone is at least, say, 12 stone.

If I know weight and height aren't independent, and I know the correlation co-efficient, can i calculate the probability a person is both at least 6ft and at least 12st?

many thanks

Originally Posted by jay4737

Hi
I am trying to find the probability of two events from two correlated normally distributed rv's. Would this be bi-variate normal and if so how would I go about calculating the probability?

To say two variables are bivariate normal then you need to calculate Mahalanobis distance.

But as you know X is normal and Y is normal then X and Y will most likely also be bivariate normal.

Be careful though, this does not work the other way around!