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February 5th, 2013, 03:05 AM   #1
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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!
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February 5th, 2013, 07:30 AM   #2
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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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