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

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 $x = 2$ and $P(2)=0.03$, the product is $2\times0.03 = 0.06$. For $x = 3$ and $P(3)=0.09$, the product is $3\times0.09 = 0.27$. For $x = 4$ and $P(4)=0.18$, the product is $4\times0.18 = 0.72$. For $x = 5$ and $P(5)=0.31$, the product is $5\times0.31 = 1.55$. For $x = 6$ and $P(6)=0.33$, the product is $6\times0.33 = 1.98$. For $x = 7$ and $P(7)=0.06$, the product is $7\times0.06 = 0.42$.

Step3: Sum up the products

$\mu=0.06 + 0.27+0.72 + 1.55+1.98+0.42$ $=5.0$

Answer:

$5.0$