Question

Outcome 0 1 5 10 1000 Probability 0.33 0.32 0.24 0.10 0.01 Which is the expected value of the random variable with the given probability distribution?

Answer 1

Answer: 12.52

Explanation:

To find the expected value, E(X), we will multiply each value of the random variable(outcome) by its probability and add the products.

The formula is given as
`E(X)=\sum xP(x)`.

Given table

Outcome 0 1 5 10 1000

Probability 0.33 0.32 0.24 0.10 0.01

`E(X) = 0*0.33+1*0.32+5*0.24+10*0.10+1000*0.01\\\\=12.52`

hence, the expected value of the random variable with the given probability distribution = 12.52