# Thread: A total of 4 buses carrying 148 student

1. ## A total of 4 buses carrying 148 student

Question : A total of 4 buses carrying 148 student from the same school arrive at a football stadium. The buses carry 40, 33, 25 and 50 students. One of the students 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.
i) Which of E[X] or E[Y] do you think is larger? Why ?
ii) Compute E[X] and E[Y]

---------------------------------------My Work-----------------------
Bus A --------Pr(Student from A) = $\frac{40}{148}$

Bus B --------Pr(Student from B) = $\frac{33}{148}$

Bus C --------Pr(Student from A) = $\frac{25}{148}$

Bus D --------Pr(Student from A) = $\frac{50}{148}$

X would be the number of student from the bus chosen

but i dont know what to do ???

2. Well, you've sussed out the distribution of students so thats a good start. Perhaps the easier start would be to list what your random variables are and their respective probabilities:

X P(X)
25 25/148
33 33/148
40 25/148
50 50/148

Y P(Y)
25 1/4
33 1/4
40 1/4
50 1/4

Do you see why?

From here it is elementary to answer parts i and ii.

3. Here i am getting

E[X] = 39.29

E[Y] = 37...................Are these correct????

4. Yes.

5. thanks mite
wish u a happy and prosporous new year
cheers