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STA260 Lecture 01
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Overview
- Source Material:
STA260H5S_Winter2026_Chapter6.pdf - Topics: Functions of a Random Sample, Point Estimation, Sampling Distributions.
- Key Theorems derived:
- Distribution of linear combinations of Normal variables.
- Sampling distribution of
(Normal population). - Unbiasedness of Sample Variance.
- Source Material:
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Core Concepts
- Random Sample: Independent and identically distributed (iid) variables.
- Linear Combination of Independent Normal Variables:
- If
are independent Normal, their linear combination is Normal. - Used to prove the distribution of
.
- If
- Sampling Distribution of the Sample Mean:
given a Normal population.
- Expectation and Variance of Sample Mean:
- Proofs that
and regardless of distribution shape.
- Proofs that
- Unbiasedness of Sample Variance:
- Proof that
.
- Proof that
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Related Distributions (Pre-Lecture)
- Chi-squared Distribution: Sum of squared standard normals; models sample variance.
- T Distribution: Sampling distribution of mean when
is unknown. - F Distribution: Ratio of two independent Chi-squared variables; compares variances.
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Footnotes