Question

find the expected value ($\mu$) of the random variable with the given probability distribution. $\mu = \square$ 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 $\mu=\sum_{i}(x_i\times P(x_i))$.

Step2: Calculate each term

For $x = 2$ and $P(2)=0.30$: $2\times0.30 = 0.6$.
For $x = 4$ and $P(4)=0.20$: $4\times0.20=0.8$.
For $x = 6$ and $P(6)=0.05$: $6\times0.05 = 0.3$.
For $x = 8$ and $P(8)=0.02$: $8\times0.02=0.16$.
For $x = 10$ and $P(10)=0.13$: $10\times0.13 = 1.3$.
For $x = 12$ and $P(12)=0.30$: $12\times0.30=3.6$.

Step3: Sum up the terms

$\mu=0.6 + 0.8+0.3+0.16+1.3+3.6$.
$\mu=6.76$.

Answer:

$6.76$