Question
The probability density function (PDF) of a sum of two independent continuous random variablesXandYis given by the convolution of the PDFs, fXandfY: fX+Y(z) = fX(x)fY(zx)dx.
- The probability density function (PDF) of a sum of two independent continuous random variablesXandYis given by the convolution of the PDFs,
fXandfY:
fX+Y(z) =
fX(x)fY(zx)dx.
Show that a sum of two independent standard normal variables results in a normal variable. Find the PDF of such a sum. Give your solutions in two ways: 1) by using the convolution function above; 2) by using moment generating functions.
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Intermediate Algebra Functions & Authentic Applications (Subscription)
Authors: Jay Lehmann
6th Edition
0134779487, 9780134779485
