Consider the Population Described by the Probability Distribution Below $\begin{array}{c|c|c|c}x & 2 & 5 & 7 \\\hline p(x) & .2 & .5 & .3\end{array}$

question 49

Essay

Consider the population described by the probability distribution below. $\begin{array}{c|c|c|c}x & 2 & 5 & 7 \\\hline p(x) & .2 & .5 & .3\end{array}$

The random variable $x$ is observed twice. The observations are independent. The different samples of size 2 and their probabilities are shown below.

Find the sampling distribution of the sample mean $\bar { x }$

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Definitions:

Mass Incarceration

The substantial increase in the number of incarcerated individuals in the prison systems of certain countries, particularly the United States.

Racial Disparity

The significant differences in treatment or outcomes between racial or ethnic groups.

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Comprised entirely of female members or participants, often highlighted in contexts where gender representation is notable.