Hyper-exponential Random Variables

**shilz222** · January 28th 2008, 09:31 PM

Lets say we want to compute the probability density function for a hyper-exponential random variable for $n = 2$ .

So $f_{X_{1} + X_{2}}(t) = \int_{0}^{t} f_{X_{1}}(s) f_{X_{2}}(t-s) \ ds$ .

Where did the $t-s$ come from?

**mr fantastic** · January 29th 2008, 01:29 AM

Originally Posted by shilz222

Lets say we want to compute the probability density function for a hyper-exponential random variable for $n = 2$ .

So $f_{X_{1} + X_{2}}(t) = \int_{0}^{t} f_{X_{1}}(s) f_{X_{2}}(t-s) \ ds$ .

Where did the $t-s$ come from?

By definition, to get $f_{X_{1} + X_{2}}(t)$ you take the convolution of $f_{X_1}$ and $f_{X_2}$ .

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