Education and Child Development

An elementary class rarely remains the same size from the beginning of the school year until the end. Families move in and out of the district, some students are reassigned, and scheduling conflicts necessitate changes. Suppose the change in the number of students in a class is a random variable with probability distribution given by

p(x) = ((|x|+1)/19))        x = -3, -2, -1, 0, 1, 2, 3

a. Verify that this is a valid probability distribution.

b. Find the mean, variance, and standard deviation of the change in class size.

c. Suppose two classes are selected at random. Find the probability that both classes remain the same size for the entire year.