.md .pdf

Convolution

If X and Y are booth random variables than \(T = X + Y\) is also random variable. Now we may want to find the PDF (PMF) \(P(T = t)\). In the case that X and Y are independent, and we know their PDF we can express:

\[ P(T = t) = \sum_x P(Y = t - x)P(X=x) = \sum_y P(X = t - y)P(Y = y) \]

Optimization in deep learning Law of total Probability