Review Erercises 951 Consider an experiment that consists of

Review Erercises 9.51 Consider an experiment that consists of 2 rolls (3. of a balanced die. If X is the number of As and Y is E. the number of 5s obtained in the 2 rolls of the die, find (a) the joint probability distribution of X and Y; 3. (b) PICX,Y) E Al, where A is the region f(z, y) l 2r at y

Solution

3.52:

The sample space S fro the three tosses of the coin is

S={HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

Let W be a random variable giving the number of heads minus the number of tails in three tosses of a coin, we assign a value of of W to each sample pointin the following way

Sample points

            HHH   3

            HHT    1

            HTH        1

            HTT   -1

            THH 1

          THT   -1

           TTH   -1

           TTT   -3

Possible values(0,-3)(1,-1)(2,1)(3,3)

P(X=0,Y=-3)=1/8

P(X=1,Y=-1)=1/8

P(X=2,Y=1)=3/8

P(X=3,Y=3)=1/8

Y/X	0	1	2	3	sum
-3	1/8	0	0	0	1/8
-1	0	3/8	0	0	3/8
1	0	0	3/8	0	3/8
3	0	0	0	1/8	1/8
sum	1/8	3/8	3/8	1/8	1