Question

9 balls are marked with the number 1, 8 balls are marked with the number 3 and 3 balls are marked with the number 5. A ball is drawn at random from the urn. If the outcome is X, what is the variance of X ?

Select one: a. 5.4000 b. 2.0400 c. 7.8000 d. 13.5600 e. 2.4000

Answer 1

Total number of balls in the urn = 9+8+3 = 2

Probability distribution table

X	1	3	5
P(x)	9/20 = 0.45	8/20 = 0.4	3/20 = 0.15

Expected value, E(x) = 1x0.45 + 3x0.4 + 5x0.15 = 2.4

Variance, V(x) = Sum of {(X - E(x))^2 x P(x)}

= (1 - 2.4)^2 x 0.45 + (3 - 2.4)^2 x 0.4 + (5 - 2.4)^2 x 0.15

= 2.04

Ans: b. 2.0400