Four buses carrying 146 high school students arrive to montreal. the buses carry, respectively, 32, 44, 28, and 42 students. one of the studetns is randomly selected. let x denote the number of students that were on the bus carrying this randomly selected student. one of the 4 bus drivers is also randomly selected. let y denote the number of students on his bus. compute the expectations and variances of x and y

The expected value of X is and the variance of X is

The expected value of Y is and the  variance of Y is

Step-by-step explanation:

(a) Let X be a discrete random variable with set of possible values D and  probability mass function p(x). The expected value, denoted by E(X) or , is

The probability mass function of X is given by

Since the bus driver is equally likely to drive any of the 4 buses, the probability mass function of Y is given by

The expected value of X is

The expected value of Y is

(b) Let X have probability mass function p(x) and expected value E(X). Then the variance of X, denoted by V(X), is

The variance of X is

The variance of Y is

4.6875 pounds

step-by-step explanation:

step-by-step explanation: