Question

The next two problems allow you to express the sum of two independent random as a precise function of each of their probability mass functions or probability density functions in the case they are each discrete or continuous random variables respectively. These problems are conceptually important because they tell you how to compute the distribution of a random walk (which we will define later) from the distribution of its steps (again, defined later) in a general case. 5. Let X, Y be independent, discrete random variables. Show that P(X + Y = z) = 〉 P(X = x)P(Y =z-x),Vz E R. XER Let X,Y be independent, continuous random variables with densities px.Py respectively. Let x+y denote the density function of the sum X+Y. Show that 6.

Answer 1