find the expected value (μ) of the random variable with the given probability distribution.\ndo not round…

Explanation:

Step1: Recall expected - value formula

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

Step2: Calculate the product for each pair

For $x = 0$ and $P(0)=0.08$, the product is $0\times0.08 = 0$. For $x = 1$ and $P(1)=0.12$, the product is $1\times0.12=0.12$. For $x = 2$ and $P(2)=0.22$, the product is $2\times0.22 = 0.44$. For $x = 3$ and $P(3)=0.24$, the product is $3\times0.24=0.72$. For $x = 4$ and $P(4)=0.18$, the product is $4\times0.18 = 0.72$. For $x = 5$ and $P(5)=0.16$, the product is $5\times0.16=0.8$.

Step3: Sum up the products

$\mu=0 + 0.12+0.44 + 0.72+0.72+0.8$ $\mu=2.8$

Answer:

$2.8$