Suppose that X and Y are conditionally independent, given Z , and X and Z are marginally independent. a. Show that X is jointly independent of Y and Z . b. Show X and Y are marginally independent. c....

Suppose thatXandYare conditionally independent, givenZ, andXandZare marginally independent.

a. Show thatXis jointly independent ofYandZ.

b. ShowXandYare marginally independent.

c. Show that ifXandZare conditionally(rather than marginally) independent, thenXandYare still marginally independent.