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Suppose a school has 20 classes: 16 with 25 students in each, three with 100 students in each, and one with 300 students for a total of 1000 students. (a) Suppose one of the 20 classes is chosen at random, let Y be the number of students in that class. Write out the p.m.f. for Y and use it to calculate the average class size at this school. (b) Suppose that one of the 1000 students is chosen at random. Let X be the size of the class to which the student belongs. Write out the p.m.f. of X and find E[X]. (c) Fill in the following: On average, a student at this school is in a class with students. On average, a class at this school has students. Comment

Given that a school has 20 classes: 16 with 25 students in each, three with 100 students in each, and one with 300 students for a total of 1000 students.

a) Y = no of students in the class out of 20 selected at random

Y can take values as

Y 25 100 300 Total

freq 16 3 1 20

P(Y) 16/20 3/20 1/20 1

y*p 20 15 15 50

E(Y) = 50

b) X = size of student from which one student is taken at random

X 25 100 300 Total

No of classes 16 3 1 20

Total students

(X*no of classes) 400 300 300 1000

P(x) 0.4 0.3 0.3 1

X*P 160 90 90 240

E(x) =240

c) On an average, a student at this school is in a class with 240 students. On average, a class at this school has 50 students.

i.e. expectation of number of students in a class is 50 while expectation of a student having students in the class is 240