Question

Sue Anne owns a medium-sized buisness. Consider the probability distribution presented below, where x describes the number of employees who cal in sick on a given day.

Number of employees sick||| 0 1   2 3   4

   p(x) | 05 .4 .3 .15 .1

Find the mean and variance of the random variable x.

Answer 1

Number of employees(X)	0	1	2	3	4
Probability	0.05	0.4	0.3	0.15	0.1

We have been given this probability distribution.

Mean or expected value= E(X)= sum(X*p(x))

= 0*0.05 + 1*0.4 + 2*0.3 + 3*0.15 + 4*0.1

= 0+0.4+0.6+0.45+0.4

= 1.85

Variance= E(X²) - [E(X)]²

Number of employees (X2)	0	1	4	9	16
Probability	0.05	0.4	0.3	0.15	0.1

Thus, E(X²)= 0*0.05 + 1*0.4 + 4*0.3 + 9*0.15 + 16*0.1

= 0+0.4+1.2+1.35+1.6

= 4.55

Thus, variance= 4.55- 1.85*1.85

= 1.1275