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 20

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.

$\begin{array}{c}\begin{array}{cc}\hline \text { Sample } &\text { Probability } \\\hline 2,2 & .04 \\2,5& .10 \\2,7 & .06\\\hline \end{array}\begin{array}{cc}\hline \text { Sample } & \text { Probability } \\\hline 5,2 & .10 \\5,5 & .25 \\5,7 & .15 \\\hline \end{array}\begin{array}{cc}\hline \text { Sample } & \text { Probability } \\\hline 7,2 & .06 \\7,5 & .15 \\7,7 & .09 \\\hline \end{array}\end{array}$



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

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Definitions:

Collar Cells

Also known as choanocytes, are flagellated cells that line the interior of asconoid sponges and are used for feeding by generating water flow and filtering food particles.

Amebocytes

Cells found in the bloodstream of invertebrates that move like amoebas, involved in various functions including distributing nutrients and forming immune responses.

Attachment

The emotional bond that develops between a child and a caregiver, influencing personal development.

Feeding

The process by which organisms obtain and consume food to sustain life.