Consider the Population Described by the Probability Distribution Below $$\begin{array} { c | c | c | c } x & 0 & 2 & 4 \\\hline p ( x ) & \frac { 1 } { 3 } & \frac { 1 } { 3 } & \frac { 1 } { 3 }\end{array}$$

question 30

Essay

Consider the population described by the probability distribution below. $$\begin{array} { c | c | c | c } x & 0 & 2 & 4 \\\hline p ( x ) & \frac { 1 } { 3 } & \frac { 1 } { 3 } & \frac { 1 } { 3 }\end{array}$$ a. Find μ. b. Find the sampling distribution of the sample mean for a random sample of n = 3 measurements from this distribution. c. Find the sampling distribution of the sample median for a random sample of n = 3 observations from this population. d. Show that both the mean and the median are unbiased estimators of μ for this population. e. Find the variances of the sampling distributions of the sample mean and the sample median. f. Which estimator would you use to estimate μ? Why? 6.3 The Sampling Distribution of x-bar and the Central Limit Theorem 1 Understand Central Limit Theorem

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Definitions:

Balance

A state of equilibrium where different elements are in the correct proportions or positions, often used in physical, psychological, and socio-economic contexts.

Reward

Something given in recognition of service, effort, or achievement.

Upward Social Comparison

The process of comparing oneself with others who are perceived to be better off or more successful, which can affect self-esteem and motivation.

Motivates

The actions or processes that stimulate someone to act towards achieving a goal or satisfying a need or desire.