Question

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

Step2: Calculate each term $x_iP(x_i)$

• For $x = - 1$ and $P(-1)=0.05$: $(-1)\times0.05=-0.05$
• For $x = 1$ and $P(1)=0.18$: $1\times0.18 = 0.18$
• For $x = 3$ and $P(3)=0.21$: $3\times0.21=0.63$
• For $x = 5$ and $P(5)=0.23$: $5\times0.23 = 1.15$
• For $x = 7$ and $P(7)=0.14$: $7\times0.14=0.98$
• For $x = 9$ and $P(9)=0.19$: $9\times0.19 = 1.71$

Step3: Sum up all the terms

$\mu=-0.05 + 0.18+0.63+1.15+0.98+1.71$
$=-0.05+(0.18 + 0.63)+(1.15+0.98)+1.71$
$=-0.05 + 0.81+2.13+1.71$
$=( - 0.05+0.81)+(2.13+1.71)$
$=0.76+3.84$
$=4.6$

Answer:

$4.6$