# Question: Two fair dice are rolled Let one of the dice

Two fair dice are rolled. Let one of the dice be red and the other green so that we can tell them apart. Let be the sum of the two values shown on the dice and be the difference (red minus green) of the two values shown on the dice. Determine whether these two random variables are independent or not. Does you answer make sense?

## Answer to relevant Questions

Starting from the general form of the joint Gaussian PDF in Equation (5.40), show that the resulting marginal PDFs are both Gaussian. In Equation 5.40 Suppose a random variable X has a CDF given by Fx (x) and similarly, a random variable Y has a CDF, Fy (y) . Prove that the function F(x,y) = Fx (x) Fy (y) satisfies all the properties required of joint CDFs and hence will ...The joint moment- generating function (MGF) for two random variables, and , is defined as Develop an equation to find the mixed moment E [Xn Ym] from the joint MGF. Suppose is a Rayleigh random variable and is an arcsine random variable, so that Furthermore, assume X and Y are independent. Find the PDF of Z = XY. Suppose and are independent discrete random variables. Find the PMF of L = M + N for each of the following cases: (a) and both follow a uniform distribution, (a) M and N both follow a uniform distribution, PM (k) = PN (k) = ...Post your question