Lecture 23 - Fall 2009

# Lecture 23 - Fall 2009 - Â 1 III Probability Random...

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Unformatted text preview: Â¡ 1 III. Probability, Random Variables and Sampling Distributions. A. Probabilty (Chapter 5) B. Random Variables (Chapter 5) C. Normal Distribution (Chapter 6) 1. Continuous Random Variables (CRVs) 2. Normally Distributed CRVs 3. Standard Normal Distribution 4. Probabilities for Any Normal Dist. 5. Determining Z-values Given Probabilities 6. Determining X-values Given Probabilities 3. Standard Normal Distribution ( 3. Standard Normal Distribution ( Z ) Â¡ Standard Normal Variable Standard Normal Variable â€“ Z Â¡ Parameters of the Standard Normal Distribution: Parameters of the Standard Normal Distribution: â€¢ Mean Mean : : Î¼ Z = 0 = 0 Ïƒ â€¢ Standard Deviation Standard Deviation : : Ïƒ Z = 1 = 1 Â¡ Probabilities Probabilities: Use the : Use the Z-Table Table . â€¢ Gives Gives cumulative probabilities cumulative probabilities : : P(Z < z) P(Z < z) the the probability that the variable probability that the variable Z is less than a specific is less than a specific value value z (you go to the table with (you go to the table with z to 2 decimals.) to 2 decimals.) Â¡ For the Standard Normal : Î¼ x = 0; Ïƒ x = 1 â€“ 68.26% of the values lie between â€“1 and +1 â€“ 95.44% of the values lie between â€“2 and +2 P(-2 < Z < 2) = 0.9544 â€“ 99.74% of the values lie between â€“3 and +3-5-4-3-2-1 1 2 3 4 5 95.44% 99.74% 68.26% Â¡...
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## This note was uploaded on 12/08/2011 for the course ECON 211 taught by Professor Daniellass during the Spring '11 term at UMass (Amherst).

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Lecture 23 - Fall 2009 - Â 1 III Probability Random...

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