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:

Moderate Intellectual Disability

A level of intellectual disability (IQ between 35 and 49) at which people can learn to care for themselves and can benefit from vocational training.

Dyslexia

A learning disorder characterized by difficulties with accurate and/or fluent word recognition, poor spelling, and decoding abilities.

Pronominal Reversal

The incorrect usage or reversal of pronouns, often observed in developmental disorders such as autism.

Echolalia

The repetition of phrases, words, or parts of words by an individual, often part of the communication patterns seen in Autism Spectrum Disorder.