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 $x = - 1$ and $P(-1)=0.12$, the product is $(-1)\times0.12=-0.12$. For $x = 1$ and $P(1)=0.18$, the product is $1\times0.18 = 0.18$. For $x = 3$ and $P(3)=0.12$, the product is $3\times0.12 = 0.36$. For $x = 5$ and $P(5)=0.28$, the product is $5\times0.28 = 1.4$. For $x = 7$ and $P(7)=0.12$, the product is $7\times0.12 = 0.84$. For $x = 9$ and $P(9)=0.18$, the product is $9\times0.18 = 1.62$.

Step3: Sum up the products

$\mu=-0.12 + 0.18+0.36 + 1.4+0.84+1.62$. $\mu=( - 0.12+0.18)+0.36 + 1.4+0.84+1.62$. $=0.06+0.36 + 1.4+0.84+1.62$. $=(0.06 + 0.36)+1.4+0.84+1.62$. $=0.42+1.4+0.84+1.62$. $=(0.42 + 1.4)+0.84+1.62$. $=1.82+0.84+1.62$. $=(1.82 + 0.84)+1.62$. $=2.66+1.62$. $=4.28$.

Answer:

$4.28$