Question

Four buses carrying 148 students from the same school arrive at a football stadium. The busescarry, respectively, 40, 33, 25, and 50 students. One of the students is randomly selected. LetXdenote the number of students that were on the bus carrying the randomly selected student. Oneof the 4 bus drivers is also randomly selected. LetYdenote the number of students on her bus.(a) Which ofE(X) orE(Y) do you think is larger? Why?(b) Find the pmf ofXandY.(c) ComputeE(X) andE(Y).

Answer 1

a. E(X) is larger

Explanation:

E(X) is larger and this is the reason why. The more the population of students in the bus, then we would have a greater likelihood of a student to be chosen randomly. But for every driver to be selected out of 4 buses, the probability of any of the buses being picked is 1/4

E(X) = (40/148*40) + (33/248*33) + (25/148*25)+(50/148*50)

= (0.279 x 40)+(0.22297*33)+(25*0.16891)+(50*0.3378)

= 39.270

E(Y) = (40x1/4)+(25*1/4)+(33*1/4)+(50*1/4)

= 40x0.25 + 33x0.25 + 25x0.25 + 50x0.25

= 37