find the expected value (μ) of the random variable with the given probability distribution. μ = ? do not…
find the expected value (μ) of the random variable with the given probability distribution. μ = ? do not round your answer.
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
$\mu=0.6 + 0.8+0.3+0.16+1.3+3.6$. $0.6+0.8 = 1.4$; $1.4+0.3=1.7$; $1.7 + 0.16=1.86$; $1.86+1.3=3.16$; $3.16+3.6 = 6.76$.
Answer:
$6.76$