Exercise 3.29. In a school there are four kindergarten classes, with 21, 24, 17 and 28 students. We choose one of the 90 kindergarten students randomly, and denote the number of students in her class by X. Find the expectation and variance of X.

Expected mean = 23.2159

Variance = 15.89

Step-by-step explanation:

Given that :

Number of kindergarten students (X) :

21 + 24 + 17 + 28 = 90

P(X):

21/ 90 = 0.233

24/90 = 0.2667

17/90 = 0.1889

28/90 = 0.3111

X : 21 24 17 28

P(x) : _ 0.233 _ 0.2667 __ 0.1889 __ 0.3111

E(X) = Σ[(p)*p(x)]

(21 * 0.233) + (24 * 0.2667) + (17 * 0.1889) + (28 * 0.3111) = 23.2159

Var(X) : Σ(x²*p(x)) - E(x)²

x² * p(x) = (21^2 * 0.233) + (24^2 * 0.2667) + (17^2 * 0.1889) + (28^2 * 0.3111) - 23.2159^2

554.8667 - 538.97801281

= 15.88868719

= 15.89