A Problem seemingly with NIntegrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg122231] A Problem seemingly with NIntegrate*From*: choco munch <choceam at gmail.com>*Date*: Fri, 21 Oct 2011 06:26:05 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

Hi, Here is my problem. I have two PDFs (Probability Density Functions). One is a sum of 2 IID Nakagami-m and the other is a zero mean Guassian. I am constructing a new RV which is the product of these two, so I have in effect: Z = (X1 + X2)*N = X12*N X1, X2 are distributed IID Nakagami and N is a zero mean Normal RV. Now I know how to compute the PDF of Z by using PDF_Z[z_] := NIntegrate[1/x PDF_X12[x]* PDF_N[z/x], {x, 0, Infinity}] Unforutantely, when i do this NIntegrate[PDF_Z[z], {z, -Infinty, Infinty}] I do not get 1. there is something going on with NIntegrate here, but I don't know what. Here is the code: ========================================================================== (*K[m] is just a constant *) K[m_] := (4 Sqrt[Pi] Gamma[2 m] m^(2 m))/(Gamma[m]^2 Gamma[2 m + 1/2] 2^(4 m - 1) \[CapitalOmega]^(2 m)); (*f1 is the sum of two Nakagami's*) f1[r_] := K[m] r^(4 m - 1) Hypergeometric1F1[2 m, 2 m + 1/2, (m r^2)/ (2 \[CapitalOmega])] Exp[-m r^2/\[CapitalOmega]] (*f2 is the standard normal *) f2[r_] := 1/(Sqrt[2 Pi] \[Sigma]) Exp[-r^2/(2 \[Sigma]^2)]; (*f3 is the product of X1+X2 and N*) f3[z_] := NIntegrate[1/x f1[x] f2[z/x], {x, 0, Infinity}] (*here is the problem*) NIntegrate[f3[x], {x, -10, 10}] (*this will not give 1, why? I have checked both f1 and f2, they are valid PDFs*)