chapter 1

Chapter 5: Joint Probability Distributions and Random Samples41.Outcome 1,1 1,2 1,3 1,4 2,1 2,2 2,3 2,4Probability .16 .12 .08 .04 .12 .09 .06 .03x 1 1.5 2 2.5 1.5 2 2.5 3r 0 1 2 3 1 0 1 2Outcome 3,1 3,2 3,3 3,4 4,1 4,2 4,3 4,4Probability .08 .06 .04 .02 .04 .03 .02 .01a.x 2 2.5 3 3.5 2.5 3 3.5 4r 2 1 0 1 3 2 1 2b. P( x ≤ 2.5)= .8x 1 1.5 2 2.5 3 3.5 4p ( x).16 .24 .25 .20 .10 .04 .01c.r 0 1 2 3p(r) .30 .40 .22 .08d. P ( X ≤ 1.5)= P(1,1,1,1) + P(2,1,1,1) + … + P(1,1,1,2) + P(1,1,2,2) + … + P(2,2,1,1) +P(3,1,1,1) + … + P(1,1,1,3)= (.4) 4 + 4(.4) 3 (.3) + 6(.4) 2 (.3) 2 + 4(.4) 2 (.2) 2 = .240042.a.x 27.75 28.0 29.7 29.95 31.65 31.9 33.64 2 6 4 8 4 2p ( x)30 30 30 30 30 30 30b.x 27.75 31.65 31.91 1 1p ( x)333c. all three values are the same: 30.4333189