y 5 10 p(x, y) 15 .02 .06 .02 .10 .04 .15 .20 .10 10 .01 .15 .14 .01

An instructor has given a short quiz consisting of nvo parts. For a randomly selected student, let X= the number of points earned on the first part and Y= the number of points earned on the second part. Suppose that thejoint pmf of X and Yis given in the accompanying table.

a. If the score recorded in the grade book is the total number of points earned on the nvo parts,what isthe expected recorded score E(X + Y)?

b. If the maximum of the two scores is recorded,what isthe expected recorded score?

A random variable is normally distributed with a mean of m =50 and a standard deviation of <T  =5.

1. Sketch a normal curve for the probability density Label the horizontal ax. is with values of 35, 40, 45, 50, 55, 60, and 65. Figure 6.4 shows that the normal curve almost touches the horizontal axis at three standard deviations below and at

three standard deviations above the mean (in this case at 35 and 65).

1. What is the probability the random variable will assume a value between 45 and 55?
2. what is the probability the random variable will assume a value between 40 and 60?