Question

Example 4.14:l The fraction X of male runners and the fraction Y of female runners who compete in marathon races are described by the joint density function CheK D 0, elsewhere. Find the covariance of X and y Solution: We first compute the marginal density functions. They are 0, elsewhere and 0, elsewhere. From these marginal density functions, we compute by inte From the joint density function given above, we have ue refills ected at ribution: Then lthough the covariance between two random variables does provide informa free. hin the magnitude ofơxv does not indi. letions

how these marginal density functions are calculated???

Answer 1

The region in which the two random variables are defined is shown as

0.8 0.6 0.4 02 1:2 陱秀 0.8 0:4 0.6 0:2 -0.2

The marginal density function of X is given by

g(x)= | 8xydy = 42.3

Thus,

40 1 g(x)={Or : g(x)0 : otherwise otherwise

The marginal pdf of Y is

h(y)- /f(x, y)dr 1 8xydz

Hence the marginal PDF is

0otherwise