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December 3rd, 2010, 06:14 PM   #1
 
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What is the probability distribution of X+Y?

Hi.. I would be grateful if anyone can solve this for me:

X1 and X2 follow the distribution:
? x exp(?0.5 ? x2) for x > 0, fX(x) = 0 for x < 0.

Given that Y=X1+X2, what is the probability distribution of Y?

Thx in advance.
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December 4th, 2010, 04:43 PM   #2
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Re: What is the probability distribution of X+Y?

Quote:
Originally Posted by ash_x
Hi.. I would be grateful if anyone can solve this for me:

X1 and X2 follow the distribution:
? x exp(?0.5 ? x2) for x > 0, fX(x) = 0 for x < 0.

Given that Y=X1+X2, what is the probability distribution of Y?

Thx in advance.
The general approach to obtain the distribution of the sum of two independent random variables is to take the convolution of the two distribution functions. Alternatively, one can calculate the characteristic functions (Fourier transforms) of the distributions, multiply them and then take the inverse transform of the product.
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