Convolution of two independent probability distributions

@Pepersteak wrote:

How would I use Math.Net to Convolve 2 independent random variables?

Assume we have two random variables X and Y
such that X∼P(x) and Y∼G(y).

We ask, what is the distribution of Z=X+Y.

If both of the distributions of X and Y
are discrete, the distribution of Z
is given by the convolution of the two, ie.
F(z)=∑ P(x)G(z−x).

Similarly, if the distributions are continuous, the convolution is
F(z)=∫ P(x)G(z−x)dx.

Also, if P(x) is discrete and the other continuous?
If P(x) is discrete, we can write it as P(x)=∑ P n δ(x−x n )
where {P n } is the probability of x n

Then,
F(z)=∫ P(x)G(z−x)dx=∑ P n G(z−x n )

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