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 $x = 0$: $0\times0.10=0$
For $x = 2$: $2\times0.35 = 0.7$
For $x = 4$: $4\times0.25=1$
For $x = 6$: $6\times0.15 = 0.9$
For $x = 8$: $8\times0.10=0.8$
For $x = 10$: $10\times0.05 = 0.5$

Step3: Sum up the terms

$\mu=0 + 0.7+1+0.9+0.8+0.5$

Answer:

$3.9$