Question

Find the expected value of the winnings
from a game that has the following
payout probability distribution:
Payout ($) 0 5
8
10
15
Probability 0.5 0.2 0.15 0.1 0.05
Expected Value = [?]

Answer 1

Multiply each payout by the corresponding probability and take the total:

E[X] = 0×0.5 + 5×0.2 + 8×0.15 + 10×0.1 + 15×0.05 = 3.95

Answer 2

The expected value = 3.92

What is expected value ?

"It describes the average of a discrete set of variables based on their associated probabilities."

Formula of expected value:

$E(x)=\Sigma[ xP(x)]$

Multiply each value of the random variable by its probability and add the products.

For given question,

We have been given a payout probability distribution.

We need to find the expected value of the winnings.

First we multiply each value of the random variable by its probability .

0 × 0.5 = 0

5 × 0.2 = 1

8 × 0.15 = 1.2

10 × 0.1 = 1

15 × 0.05 = 0.75

Now, we find the sum of above products.

0 + 1 + 1.2 + 1 + 0.75 = 3.95

By using the formula of expected value,

$\Rightarrow E(x)=\Sigma[ xP(x)]\\\\\Rightarrow E(x)=3.92$

Therefore, the expected value = 3.92

Learn more about the expected value here:

https://brainly.com/question/18523098

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