find the expected value ($\mu$) of the random variable with the given probability distribution. do not round your answer

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Accepted Answer

# Explanation:
## Step1: Recall the formula for expected value
The formula for the expected value $\mu$ of a discrete random variable is $\mu=\sum_{i}x_{i}P(x_{i})$, where $x_{i}$ are the values of the random variable and $P(x_{i})$ are their corresponding probabilities.
## Step2: Calculate each term $x_{i}P(x_{i})$
- For $x = 2$ and $P(2)=0.03$: $2\times0.03 = 0.06$
- For $x = 3$ and $P(3)=0.09$: $3\times0.09=0.27$
- For $x = 4$ and $P(4)=0.18$: $4\times0.18 = 0.72$
- For $x = 5$ and $P(5)=0.31$: $5\times0.31=1.55$
- For $x = 6$ and $P(6)=0.33$: $6\times0.33 = 1.98$
- For $x = 7$ and $P(7)=0.06$: $7\times0.06=0.42$
## Step3: Sum up the terms
$\mu=0.06 + 0.27+0.72 + 1.55+1.98+0.42$
$$
\begin{align*}
\mu&=(0.06+0.27)+0.72 + 1.55+1.98+0.42\
&=0.33+0.72+1.55 + 1.98+0.42\
&=(0.33+0.72)+1.55+1.98+0.42\
&=1.05+1.55+1.98+0.42\
&=(1.05 + 1.55)+1.98+0.42\
&=2.6+1.98+0.42\
&=(2.6+1.98)+0.42\
&=4.58+0.42\
&=5
\end{align*}
$$

# Answer:
$5$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for expected value

Step2: Calculate each term \(x_{i}P(x_{i})\)

Step3: Sum up the terms

Answer: