Answer:
V(X)= 39.10
V(Y)= 40
Step-by-step explanation:
Given that
Total number of student = 140
Bus A - 31
Bus B- 43
Bus C- 27
Bus D- 39
The probability that a student was on the bus is proportional to the number of student. Eg 31/140 in bus A, 43/140 on bus B, ...
E(X) = (31*31/140) + (43*43/140) + (27*27/140) + (39*39/140)
= 35.5
V(X)= 39.10
The bus driver have 1/4 probability on being on any of the buses.
E(Y) = 140/4 = 35
V(Y)= 40