Convolution of two densities

Graphs, Integrals, probability, density function (Gaussian, uniform, tent and parabolic)The convolution of two functions can be thought of as a measure of the overlap of the graphs as one graph is shifted horizontally across the other. Formally, if f and g are functions, the convolution of the two is the function (f*g)(t) = ∫f(t-τ)g(τ)dτ from -∞ to ∞ The plot shows f(t-τ), that is, f shifted by t units, in blue, g(τ) in purple, and the product of the two in gold. Thus the gray area is exactly the value of the convolution at t. If X and Y are independent random variables with respective density functions f and g, then the density function of X+Y is the convolution of f and g. Interestingly, the convolution of two Gaussian densities is a Gaussian densityComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemátic