Question

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

x: 5, 6, 8, 14
p(x): 0.4, 0.2, 0.2, 0.2

a. the average value of x over many trials will be less than μ
b. the average value of x over many trials will be more than μ
c. the average value of x over many trials is equal to μ

in this case, can the random variable x ever assume the value μ?
options: yes, no

Explanation:

First, we need to calculate the mean (μ) of the random variable \( x \). The formula for the mean of a discrete random variable is \( \mu = \sum x \cdot P(x) \).

Given the values of \( x \) as 5, 6, 8, 14 and their corresponding probabilities \( P(x) \) as 0.4, 0.2, 0.2, 0.2 respectively.

Calculating \( \mu \):

$$
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Now, check if \( x \) can assume the value of \( \mu = 7.6 \). The possible values of \( x \) are 5, 6, 8, 14. None of these values is equal to 7.6. So the random variable \( x \) can never assume the value \( \mu \).

Answer:

No