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 $\mu=\sum_{i}x_iP(x_i)$.

Step2: Calculate each term

For $x = 1$: $1\times0.03=0.03$.
For $x = 2$: $2\times0.11 = 0.22$.
For $x = 3$: $3\times0.13=0.39$.
For $x = 4$: $4\times0.25 = 1$.
For $x = 5$: $5\times0.32=1.6$.
For $x = 6$: $6\times0.16 = 0.96$.

Step3: Sum up the terms

$\mu=0.03 + 0.22+0.39+1+1.6+0.96$.
$0.03+0.22 = 0.25$.
$0.25+0.39 = 0.64$.
$0.64 + 1=1.64$.
$1.64+1.6 = 3.24$.
$3.24+0.96=4.2$.

Answer:

$4.2$