Question

consider the probability distribution shown for the random variable x found below. complete part a through f.

x	5	6	8	14

...

a. find \\( \mu = e(x) \\).
\\( \mu = \square \\) (round to the nearest tenth as needed )

Explanation:

Step1: Recall the formula for expected value

The expected value \( \mu = E(x) \) of a discrete random variable is calculated as \( \mu=\sum x \cdot p(x) \), where \( x \) are the values of the random variable and \( p(x) \) are their corresponding probabilities.

Step2: Multiply each \( x \) by its \( p(x) \)

For \( x = 5 \) and \( p(x)=0.4 \): \( 5\times0.4 = 2 \)
For \( x = 6 \) and \( p(x)=0.2 \): \( 6\times0.2 = 1.2 \)
For \( x = 8 \) and \( p(x)=0.2 \): \( 8\times0.2 = 1.6 \)
For \( x = 14 \) and \( p(x)=0.2 \): \( 14\times0.2 = 2.8 \)

Step3: Sum the products

Add the results from Step 2: \( 2 + 1.2+1.6 + 2.8=7.6 \)

Answer:

\( \mu = 7.6 \)