Sample Question #180 (probability theory)

Consider two independent random variables *X *and *Y.** *What’s the **pdf **of *X+Y*?

(Comment: how’s this question different from the previous one, #179?)

Advertisements

Sample Question #180 (probability theory)

Consider two independent random variables *X *and *Y.** *What’s the **pdf **of *X+Y*?

(Comment: how’s this question different from the previous one, #179?)

Advertisements

%d bloggers like this:

ANSWER

The derivation is not quite straightforward, so you should just remember the result: the pdf of the sum of two independent variables is the convolution of their individual pdf’s. Let the two pdf’s be f(x) and g(y) respectively. The pdf of Z=X+Y is

h(z) = integral (from -inf to +inf) { f(v)g(z-v) } dv

More discussions can be found here.