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

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Apr 14, 2023 124 likes •235 views

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

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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

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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.

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

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

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Expected payout per ticket is $4.59

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

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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

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Playing the Optimal Strategy (Return 100.762%)

What is the Daily Distribution of Winnings/Losses? Sample Size n=4800

600 hands an hour
8 hours a day

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Playing the Optimal Strategy (Return 100.762%)

What is the Yearly Income Distribution? Sample Size n=1,440,000

600 hands an hour
8 hours a day
300 Days a Year