Question

4) (30 POINTS TOTAL) X an Y are discrete random variable; X has sample space 1,21 and Y has sample space 1O,1 Table1 shows the joint distribution of (X,) TABLE 1. Joint p.mf. DANIEL TANNEN BAUM (a) (5 points) C(mpute the! luarginal distribution ofヱand y, i e can plete the following table 0 P(x) (b) (5 points) Cakulate the expectation of y. E (c) (5 points) Caleulate the conditional distribtion of y e. caleulate pyr) r each value ofr. Hint: yota are looking for Pr(y = 1|& 1), Pr(y = 이ヱ= 1), Pr(y = 1|e = 2), and Pr(y = 0|& = 2) (d) (5 points) Cakulate the conditional expectation E y r at each value of r, i e. E y r = 1) and Ely(z = 2] (e) (5 points) Caleulate the expectation of the conditional expectation fanction over the distributon of : where! í indeses the! ek ments of the sample space! ofヱ () (5 points) Compare your answrs for parts () and ). What s the theorem that characterias this relatonship?

Answer 1