[R] integration of two normal density

Bill.Venables at csiro.au Bill.Venables at csiro.au
Sat Jun 26 07:52:58 CEST 2010

Your intuition is wrong and R is right.

Why should the product of two probability density functions be a normalized pdf also? 

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of Carrie Li
Sent: Saturday, 26 June 2010 1:28 PM
To: r-help
Subject: [R] integration of two normal density

Hello everyone,

I have a question about integration of two density function
Intuitively, I think the value after integration should be 1, but they are
not. Am I missing something here ?

> t <- function(y){dnorm(y, mean=3)*dnorm(y/2, mean=1.5)}
> integrate(t, -Inf, Inf)
0.3568248 with absolute error < 4.9e-06

Also, is there any R function or package could do multivariate integration ?

Thanks for any suggestions!


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