Question

In a certain animal​ species, the probability that a healthy adult female will have no offspring in a given year is 0.24, while the probabilities of​ 1, 2,​ 3, or 4 offspring​ are respectively 0.25, 0.19, 0.17, and 0.15. Find the expected number of offspring. ​

Answer 1

The expected number of offspring is 2

Explanation:

The given parameters can be represented as:

`\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.24} & {0.25} & {0.19} & {0.17} & {0.15} \ \end{array}`

Required

The expected number of offspring

This implies that we calculate the expected value of the function.

So, we have:

`E(x) = \sum x * P(x)`

Substitute known values

`E(x) = 0 * 0.24 + 1 * 0.25 + 2 * 0.19+ 3 * 0.17 + 4 * 0.15`

Using a calculator, we have:

`E(x) = 1.74`

`E(x) = 2` --- approximated