Question

find the expected value ($\mu$) of the random variable with the given probability distribution.
$\mu =$
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 $x = - 3$ and $P=-0.02$: $(-3)\times0.02=-0.06$.
• For $x=-1$ and $P = 0.34$: $(-1)\times0.34=-0.34$.
• For $x = 1$ and $P=0.41$: $1\times0.41 = 0.41$.
• For $x = 3$ and $P=0.15$: $3\times0.15=0.45$.
• For $x = 5$ and $P=0.04$: $5\times0.04 = 0.2$.
• For $x = 7$ and $P=0.02$: $7\times0.02=0.14$.

Step3: Sum up the terms

$\mu=-0.06+( - 0.34)+0.41 + 0.45+0.2+0.14$.
$\mu=(-0.06-0.34)+(0.41 + 0.45+0.2+0.14)$.
$\mu=-0.4+(1.2)$.

Answer:

$0.8$