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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 . But in this case you do not need to as the density is obviously: , where is the pdf of CB 

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