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STAT 3743 Daily Outline

STAT 3743 Daily Outline

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2010-10-18 Mon

Mean and variance of X-bar

MGF of linear combination of independent sample

MGF of X-bar

Example: SRS(11) from gamma, find dist'n of X-bar

Proposition: SRS(n) from norm, then X-bar is normal, too

Sum of independent chisq is chisq, and df's add

Sum of squared standard normals is chisq with df = n

Theorem: SRS(n) from norm, then

  1. X-bar and S2 are independent
  2. S2 is scaled chisq with df = n - 1

Linear combinations of independent normals is normal, too

Central Limit Theorem

statement of the theorem

Remarks:

  • if X's are normal, then X-bar is normal
  • if X's are close to normal, then X-bar is close to normal, too
  • Discrete/continuous doesn't matter
  • how large is large?

Author: G. Jay Kerns

Date: 2010-11-05 14:44:11 EDT

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