Question

members of a step team perform dances involving stepping and clapping in unison. the random variable x represents the number of years of stepping experience that each member of the team has. the probability distribution, p(x), for the random variable x is shown on the graph below. what is the mean of the probability distribution?

Explanation:

Step1: Recall mean formula for discrete - random variable

The mean $\mu$ of a discrete - random variable $X$ is given by $\mu=\sum_{x}x\cdot P(x)$, where $x$ are the values of the random variable and $P(x)$ are their corresponding probabilities.
From the graph:
When $x = 1$, $P(1)=0.3$; when $x = 2$, $P(2)=0.4$; when $x = 3$, $P(3)=0.1$; when $x = 4$, $P(4)=0$; when $x = 5$, $P(5)=0.2$.

Step2: Calculate the product for each $x$ and $P(x)$

For $x = 1$: $1\times0.3 = 0.3$
For $x = 2$: $2\times0.4=0.8$
For $x = 3$: $3\times0.1 = 0.3$
For $x = 4$: $4\times0=0$
For $x = 5$: $5\times0.2 = 1$

Step3: Sum up the products

$\mu=0.3 + 0.8+0.3 + 0+1$
$\mu=2.4$

Answer:

$2.4$