Isn't it equally trivial to demonstrate that the product of two pdfs _may_ be a normalized pdf? For example, the uniform (0,1) pdf:
f(x) = 1 for x in (0, 1), and 0 otherwise Hence, g(x) = f(x)*f(x) = 1 for x in (0, 1), and 0 otherwise _is_ a normalized pdf. But this is a little silly. Rather than memorize answers to questions like "is the product of pdfs also a pdf?", we ought to be confident in the properties of pdfs (i.e. not the answers, but the means to arrive at answers). On Mon, 2010-06-28 at 11:42 -0400, Bert Gunter wrote: > Inline Below > > Bert Gunter > Genentech Nonclinical Biostatistics > > -----Original Message----- > From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On > Behalf Of bill.venab...@csiro.au > Sent: Friday, June 25, 2010 10:53 PM > To: carrieands...@gmail.com; R-help@r-project.org > Subject: Re: [R] integration of two normal density > > Your intuition is wrong and R is right. > > Why should the product of two probability density functions be a normalized > pdf also? > > -- as is trivially seen with two uniforms on [0,2], with pdf= 1/2, product = > 1/4 on [0,2] . > > -- Bert > > -----Original Message----- > From: r-help-boun...@r-project.org [mailto:r-help-boun...@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! > > Carrie > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. -- Matthew S. Shotwell Graduate Student Division of Biostatistics and Epidemiology Medical University of South Carolina http://biostatmatt.com ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
