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Suppose 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) What is the average class size? (b) Select a student randomly out of the 1000 students. Let the random variable X equal the size of the class to which this student belongs, and define the pmf of X. (c) Find E(X), the expected value of X. Does this answer surprise you?

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Answer

a)   y    |      p(y)

    25   |      0.8

   100   |     0.15

   300   |      0.05

E(y) = ∑ y . p(y)

E(y) = 25 × 0.8 + 100 × 0.15 + 300 × 0.05

E(y) = 50

average class size equal to E(y) = 50

b)  y    |      p(y)

    25   |     [tex]\dfrac{16\times 25}{1000}=0.4[/tex]

   100   |     [tex]\dfrac{3\times 100}{1000}=0.3[/tex]

   300   |      [tex]\dfrac{1\times 300}{1000}=0.3[/tex]

E(y) = ∑ y . p(y)

E(y) = 25 × 0.4 + 100 × 0.3 + 300 × 0.3

E(y) = 130

average class size equal to E(y) = 130

c) Average Student in the class in a school = 50

  Average student at the school has student = 130

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