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 February 5th, 2013, 02:05 AM #1 Newbie   Joined: Feb 2013 Posts: 2 Thanks: 0 sum of two variables Hi, Can any of you help me? I have some problem with this exercise of "probability and statistics" : Calculate the probability density function (PDF) of Z=X+Y where Y is discrete random variable which is be equal to -1,1 with equal probability; X is standard gaussian random variable independent from Y. ///// I know that the PDF of sum of two independent variables is given by the convolution of the marginal PDF fz(z)=fx*fy but if one on the two variables is discrete what should I do? Thanks all!
 February 5th, 2013, 06:30 AM #2 Senior Member   Joined: Jan 2012 From: Erewhon Posts: 245 Thanks: 112 Re: sum of two variables This can stil be done as a convolution using delta functions, so that the pdf of the discrete distribution is $(1/2)\delta(x+1)+(1/2)\delta(x-1)$. But in this case you do not need to as the density is obviously: $f(x)= (1/2)p(x, -1, 1) +(1/2) p(x,1,1)$, where $p(x,\mu,\sigma^2)$ is the pdf of $N(\mu,\sigma^2)$ CB

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