Question

In a certain animal species, the probability that a healthy adult fernale will have no offspring in a given year is 0.24, while the probabilities of 1, 2, 3, 4 offspring are,respectively, 0.24,0,19,0.18, and 0.15. Find the expected number of offspring.Elx)=(Round to two decimal places as needed.)

Answer 1

E[X] = 1.76

Step-by-step explanation

The expected value of a discrete data set is the sum of the products of each value by its probability. We have in this case:

• P(0) = 0.24

,

• P(1) = 0.24

,

• P(2) = 0.19

,

• P(3) = 0.18

,

• P(4) = 0.15

The expected value in this problem is:

`\begin{gathered} E\lbrack X\rbrack=0\cdot0.24+1\cdot0.24+2\cdot0.19+3\cdot0.18+4\cdot0.15 \\ E\lbrack X\rbrack=0+0.24+0.38+0.54+0.6 \\ E\lbrack X\rbrack=1.76 \end{gathered}`