Show that the two random variables X 1 and X 2 considered in exercise 5.7 are independent if…

Show that the two random variables X1 and X2 considered in exercise 5.7 are independent if their joint probability mass function is given by Table 5A, and are dependent if their joint probability mass function is given by Table 5B.

Exercise 5.7

In exercises consider 2 random variables, X1 and X2, with the joint probability law specified by the probability mass function PX1, X2 (. , .) given for all X1 and x2 at which it is positive by (a) Table 5A, (b) Table 5B, in which for brevity we write h for to.

 

Show that the individual probability mass functions of X1 and X2 may be obtained by summing the respective columns and rows as indicated. Are X1 and X2 (i) jointly discrete, (ii) individually discrete?

 

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