Example 9.3: Let X1, X2, ..., Xn be a random sample from a population mean and variance o². Show that the sample variance, S² - Σ(x₁ - x)²
Example 9.3: Let X1, X2, ..., Xn be a random sample from a population mean and variance o². Show that the sample variance, S² - Σ(x₁ - x)²
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![**Example 9.3**: Let \( X_1, X_2, \ldots, X_n \) be a random sample from a population mean \( \mu \) and variance \( \sigma^2 \). Show that the sample variance,
\[
S^2 = \frac{\sum (X_i - \overline{X})^2}{n-1}
\]
is an unbiased estimator of \( \sigma^2 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F243a7230-816a-40d0-9f50-4da38fdaa0a6%2Fd2d5413a-d64e-4fcf-b912-aadfecae8573%2F9fxsm3v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Example 9.3**: Let \( X_1, X_2, \ldots, X_n \) be a random sample from a population mean \( \mu \) and variance \( \sigma^2 \). Show that the sample variance,
\[
S^2 = \frac{\sum (X_i - \overline{X})^2}{n-1}
\]
is an unbiased estimator of \( \sigma^2 \).
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