Question

find the expected value (μ) of the random variable with the given probability distribution. μ = ? do not round your answer.

Explanation:

Step1: Recall the formula for expected value

The formula for the expected value $\mu$ of a discrete random variable is $\mu=\sum_{i}x_iP(x_i)$.

Step2: Calculate each term

For $x = 0$: $0\times0.36=0$.
For $x = 2$: $2\times0.25 = 0.5$.
For $x = 4$: $4\times0.16=0.64$.
For $x = 6$: $6\times0.09 = 0.54$.
For $x = 8$: $8\times0.09=0.72$.
For $x = 10$: $10\times0.05 = 0.5$.

Step3: Sum up the terms

$\mu=0 + 0.5+0.64 + 0.54+0.72+0.5$.
$\mu=2.9$.

Answer:

$2.9$