# Thread: Bivariate normal distribution - Conditional probability P(|X|>x and |Y|>y)

1. ## Bivariate normal distribution - Conditional probability P(|X|>x and |Y|>y)

Hey folks!

Are you able to provide a suitable reference (book, article, class notes, examples in R) to compute the

P(|X|>x and |Y|>y)?

Give thant X and Y ~BVN(mu1, mu2, sigma1, sigma2, rho) ?

X and Y are actually standard normal variables with mean 0 and variance 1. The correlation is known, say, rho, and rho > 0.

Sorry for my bad notation. My background in statistics is very limited.

Thanks.

Wallace

2. ## Re: Bivariate normal distribution - Conditional probability P(|X|>x and |Y|>y)

Hey DerWundermann.

Just make the limits what they should be and partition them out.

In one dimension you have Integral (a,b) f(x)dx + Integral (c,d) f(x)dx where a=-infinity,d=+infinity and a = -c gives P(|X| > a).

You can apply the same idea except you are working on a two dimensional region instead of a one dimensional one.

If there is no covariance between the two random variables then you will exclude a rectangle at the centre from your probability.

If there is covariance structure, you will need to calculate your limits in a different way depending on the covariance.

3. ## Re: Bivariate normal distribution - Conditional probability P(|X|>x and |Y|>y)

Many thanks, Chiro!

I will to digest your recommedation!