NW 5.10 Consider the following probability distribution: Xx p(x) 0 -102 3 1 com 3 2 mean and the sample median. f. Which estimator would you use to estimate ? Why? 3 a. Find μ. b. For a random sample of n = 3 observations from this distribution, find the sampling distribution of the sample mean. c. Find the sampling distribution of the median of a sample of n = 3 observations from this population. d. Refer to parts b and c, and show that both the mean and median are unbiased estimators of μ for this population. e. Find the variances of the sampling distributions of the sample
NW 5.10 Consider the following probability distribution: Xx p(x) 0 -102 3 1 com 3 2 mean and the sample median. f. Which estimator would you use to estimate ? Why? 3 a. Find μ. b. For a random sample of n = 3 observations from this distribution, find the sampling distribution of the sample mean. c. Find the sampling distribution of the median of a sample of n = 3 observations from this population. d. Refer to parts b and c, and show that both the mean and median are unbiased estimators of μ for this population. e. Find the variances of the sampling distributions of the sample
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
only part c and e
Transcribed Image Text:## Probability Distribution Problem
### Consider the following probability distribution:
| \( x \) | 0 | 1 | 2 |
|---------|-----|-----|-----|
| \( p(x) \) | \( \frac{1}{3} \) | \( \frac{1}{3} \) | \( \frac{1}{3} \) |
---
### Questions:
a. **Find \( \mu \).**
b. **For a random sample of \( n = 3 \) observations from this distribution, find the sampling distribution of the sample mean.**
c. **Find the sampling distribution of the median of a sample of \( n = 3 \) observations from this population.**
d. **Refer to parts b and c, and show that both the mean and median are unbiased estimators of \( \mu \) 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 \( \mu \)? Why?**
---
This exercise involves working with a simple probability distribution and examining the properties of sample means and medians as estimators of the population mean \( \mu \).
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