Question

A discrete random variable X has the following probability distribution: 

x	77	78	79	80	81
P(x)	0.15	0.15	0.20	0.40	0.10

Compute each of the following quantities.

 i. P(X = 80)

 ii. P(x > 80)

 iii. P(X ≤ 80) 

 iv. The mean, μ of x. 

 v. The variance, σ² of X. 

vi. The standard deviation, σ of X.

Answer 1

i) P(X = 80) = 0.40

ii) P(X > 80) = P(X = 81) = 0.10

iii) P(X ≤ 80) = 1 - P(X > 80) = 0.90

iv) The mean of X, = = 77*0.15 + 78*0.15 + 78*0.20 + 80*0.40 + 81*0.10 = 78.95

v) The variance of X,

= 33.1475

vi) The standard deviation, of X = √33.1475 = 5.757