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Unformatted text preview: 1 CHAPTER 7: DISCRETE PROBABILITY DISTRIBUTIONS Stats & Prob. for Bus. Mgmt (Stat1100) Jochem Chap 7: Discrete Prob. Distributions b Overview b 1. Random Variables b 2. Probability Distributions . Bivariate Distributions 2 b 3. Bivariate Distributions b 4. Binomial Distributions b 5. Poisson Distribution b 1.2 Random Variables (RVs) b A RV is a function that assigns a number to each outcome of an experiment. (We usually use capital letters X,Y or Z to refer to a RV.) 3 Chap 7: Discrete Prob. Distributions b A discrete RV is one where the outcomes are countable. An RV where the outcomes are uncountable is called continuous. s Discrete RV: Sum of rolling 2 dice. s Continuous RV: Time to finish a problem set. s E.g., For any 2 lengths there is a length in between. (The same with time or weight.) We’ll look at continuous RVs in Chapter 8.. 1 st die B 4 b 1.2 Random Variables (RVs) b Example 1: Let RV X be the sum of 2 dice: : 1 Chap 7: Discrete Prob. Distributions 1 die B ↓ 2 nd die 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4 5 6 7 8 3 4 5 6 7 8 9 4 5 6 7 8 9 10 5 6 7 8 9 10 11 6 7 8 9 10 11 12 36 possible sum outcomes 2: 1 3: 2 4: 3 5: 4 6: 5 7 : 6 8: 5 9: 4 10:3 11:2 12 : 1 X = Sum =36 RV is a function: input: outcome of the experiment output: frequency of the outcomes. Examples:1 poss. of getting12 6 poss. of getting 7. X( 7 ) = 6 X( 12 ) = 1 5 b 1. Random Variables (RVs) b The probability of an RV’s outcome is written as P(X=x) or simply as P(x). x X (x) P(x) he column P(x) is called the “ robability Chap 7: Discrete Prob. Distributions B P(X=7) = P(7) = 6/36 . B P(X=12) = P(12) = 1/36 . s Example: 2 1 1/36 3 2 2/36 4 3 3/36 5 4 4/36 6 5 5/36 7 6 6/36 8 5 5/36 9 4 4/36 10 3 3/36 11 2 2/36 12 1 1/36 The column P(x) is called the “probability distribution ” of a discrete RV. We obtain the probability distribution by using the “classical approach” to assign probabilities. (In other words, we know that with a fair die, each outcome is equally likely.) 6 b 1. Random Variables (RVs) b Example 2: s Let X = the number of girls born to a family with 3 kids. s Suppose getting a girl has a probability of 0.52. Chap 7: Discrete Prob. Distributions s B Find the RV and its probability distribution. (Hint: Draw a probability tree.) Suppose we got this probability using the relative frequency approach to assigning probability. 7 b 1. Random Variables (RVs) b Example 2: s Let X = the number of girls born to a family with 3 kids. s Suppose getting a girl has a probability of 0.52. Chap 7: Discrete Prob. Distributions s B Find the RV and its probability distribution. (Hint: Draw a probability tree.) X = P(x) = 0: 1 (BBB) 1: 3 (GBB, BGB, BBG) 2: 3 (GGB, GBG, BGG) 3: 1 (GGG) 0: 1*0.48^3 = 11.1% 1: 3*0.52^1*0.48^2= 35.9% 2: 3*0.52^2*0.48^1= 38.9% 3: `1*0.52^3 = 14.1% Sum =100% Suppose we got this probability using the relative frequency approach to assigning probability....
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This note was uploaded on 03/26/2012 for the course STAT 1100 taught by Professor Chiappetta during the Spring '08 term at Pittsburgh.
 Spring '08
 Chiappetta
 Binomial, Poisson Distribution, Probability

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