THE CENTRAL LIMIT THEOREM- WHAT SAMPLE SIZE IS NEEDED? PAUL - PowerPoint PPT Presentation

THE CENTRAL LIMIT THEOREM- WHAT SAMPLE SIZE IS NEEDED? PAUL BOUTHELLIER DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE UNIVERSITY OF PITTSBURGH-TITUSVILLE TITUSVILLE, PA 16354 PBOUTHE@PITT.EDU

The central limit theorem (CLT) states that the distribution of sample means approximates a normal distribution as the sample size gets larger. Sample sizes equal to or greater than 30 are considered sufficient for the CLT to hold.

Shall Look At: n≥30 Does Not Work For Highly Skewed Distributions And Our Sample Sizes Just Cannot Approach Infinity

THE PROBABILITY OF POKER HANDS & PROGRAMMING SIMULATION OF SIZE N=1,000,000

Expected payout per ticket is $4.59

EXPECTED VALUES OF PAYOUTS FOR N=1000 RUNS OF N=1,000,000 POKER HANDS

VIDEO POKER: DEUCES WILD ROYAL FLUSH 800 FOUR DEUCES 200 WILD ROYAL FLUSH 25 FIVE OF A KIND 15 STRIGHT FLUSH 9 FOUR OF A KIND 5 FULL HOUSE 3 FLUSH 2 STRIGHT 2 THREE OF A KIND 1

Playing the Optimal Strategy (Return 100.762%) 600 hands an hour • 8 hours a day • What is the Daily Distribution of Winnings/Losses? Sample Size n=4800

Playing the Optimal Strategy (Return 100.762%) 600 hands an hour • 8 hours a day • 300 Days a Year • What is the Yearly Income Distribution? Sample Size n=1,440,000