# Question: Show that the concept of total probability can be extended

Show that the concept of total probability can be extended to expected values. That is, if {Ai}, i = 1,2,3, …, n is a set of mutually exclusive and exhaustive events, then

## Answer to relevant Questions

Find the mean of the random variables described by each of the following cumulative distribution functions: (a) (b) (c) (d) Suppose X is uniformly distributed over (– a, a), where a is some positive constant. Find the PDF of Y= X2. A real number between 0 and l00 is randomly selected according to a uniform distribution and rounded off to the nearest integer. For example, 36.5001 is rounded off to 37; √3 is rounded off to 2; and 69.49 is rounded off ...A pair of random variables, (X, Y), is equally likely to fall anywhere within the region defined by |X| + |Y| ≤ 1. (a) Write the form of the joint PDF, fX,Y (x,y). (b) Find the marginal PDFs, fX (x) and fY (y). (c) Find ...Suppose a pair of random variables is uniformly distributed over a rectangular region, A: x1 < X < x2, y1 < Y < y2. Find the conditional PDF (X, Y) of given the conditioning event (X, Y) Ɛ B, where the region B is an ...Post your question