65 The number of pizzas delivered to university students eac

6.5.

The number of pizzas delivered to university students each month is a random variable with the following probability distribution.

0

.1

1

.3

2

.4

3

.2

a.

Find the probability that a student has received delivery of two or more pizzas this month.

b.

Determine the mean and variance of the number of pizzas delivered to students each month.

Solution

more than 2 will take into consideration the case of pixxa 2 and pizza 3 in a month

a) P(x >= 2) = P(x = 2) + P(x = 3) = 0.4 + 0.2 = 0.6

b) Mean = Sum x*P(x) = 0*0.1 + 1*0.3 + 2*0.4 + 3*0.2 = 1.7

Variance = [Sum (x^2)*P(x)] - Mean^2

= [ 0*0.01 + 1*0.3 + 4*0.4 +9*0.2] - 1.7

= 2