Question

Let random variable X take the values 5, 5 and 12 with respective probabilities 0.2, 0.4 and 0.4.

a.What is the expected value of X?

b.What is the variance of X?

c.What is the standard deviation of X?

Answer 1

a) Expected value of X= E(X)= Value * probability of having that value=

=5*0.2 + 5*0.4 + 12*0.4

= 1+2+4.8

= 7.8

b) Variance of X= var(X) = E(X²)-(E(X))²

E(X)²= 5²*0.2 + 5²*0.4 + 12²*0.4 = 25*0.2 + 25*0.4 + 144*0.4 = 72.6

Var(X)= 72.6 - 7.8² =72.6-60.84 = 11.76

c) Standard deviation of X = sd(X) = (var(X))^0.5 = (11.76)^0.5 = 3.429