how long would you expect a new hire to stay with the company?

Question

A company wants to evaluate its attrition rate, in other words, how long new hires stay with the company. Over the years, they have established the following probability distribution.

Let X = the number of years a new hire will stay with the company.

Let P(x) = the probability that a new hire will stay with the company x years.

On average, how long would you expect a new hire to stay with the company? (Enter an exact number as an integer, fraction, or decimal.)

_____ yr

x P(x)

0	0.12
1	0.18
2	0.30
3	0.15
4
5	0.10
6	0.05

Answer 1

You just need the expected value of x

This is 0 x 0.12 + 1 x 0.18 + 2 x 0.30 + 3 x 0.15 + 4 x 0.10 + 5 x 0.10 + 6 x 0.05 = 2.43 years

In other words if you sample N new hires (where N is large > 1000), the mean number of years they stay would be approx 2.43 (this is following the Law of large numbers).

MIKE