BAD 200 Study Guide - Final Guide: Marginal Distribution
6 Nov 2020
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In exercise 5. 65, we considered random variables y1 and y2 that, for "1 1, have joint density function given by and established that the marginal distributions of y1 and y2 are both exponential with mean 1. Suppose that, for "1 1, the probability density function of (y1, y2) is given by a show that the marginal distribution of y1 is exponential with mean 1. 1 c show that y1 and y2 are independent if and only if = 0. Notice that these results imply that there are infinitely many joint densities such that both marginals are exponential with mean 1. From the information, observe that the probability density functions of for is as follows: Substitute in the equation (1) to get the required value. Substitute in the equation (2) to get the required value. The calculation of the second part is as follows:
