usingprobabilityandprobabilitydistributions(编辑修改稿)

usingprobabilityandprobabilitydistributions(编辑修改稿)内容摘要：

1 for each xi  S P(xi) = 1 Discrete Probability Distribution Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 433 Discrete Random Variable Summary Measures  Expected Value of a discrete distribution (Weighted Average) E(x) = Sxi P(xi)  Example: Toss 2 coins, x = of heads, pute expected value of x: E(x) = (0 x .25) + (1 x .50) + (2 x .25) = x P(x) 0 .25 1 .50 2 .25 Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 434  Standard Deviation of a discrete distribution where: E(x) = Expected value of the random variable x = Values of the random variable P(x) = Probability of the random variable having the value of x Discrete Random Variable Summary Measures P( x )E( x )}{xσ 2x  (continued) Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 435  Example: Toss 2 coins, x = heads, pute standard deviation (recall E(x) = 1) Discrete Random Variable Summary Measures P( x )E( x )}{xσ 2x  . 7 0 7. 5 0(. 2 5 )1)(2(. 5 0 )1)(1(. 2 5 )1)(0σ 222x (continued) Possible number of heads = 0, 1, or 2 Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 436 Two Discrete Random Variables  Expected value of the sum of two discrete random variables: E(x + y) = E(x) + E(y) = S x P(x) + S y P(y) (The expected value of the sum of two random variables is the sum of the two expected values) Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 437 Covariance  Covariance between two discrete random variables: σxy = S [xi – E(x)][yj – E(y)]P(xiyj) where: xi = possible values of the x discrete random variable yj = possible values of the y discrete random variable P(xi ,yj) = joint probability of the values of xi and yj occurring Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 438  Covariance between two discrete random variables: xy 0 x and y tend to move in the same direction xy 0 x and y tend to move in opposite directions xy = 0 x and y do not move closely together Interpreting Covariance Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 439 Correlation Coefficient  The Correlation Coefficient shows the strength of the linear association between two variables where: ρ = correlation coefficient (“rho”) σxy = covariance between x and y σx = standard deviation of variable x σy = standard deviation of variable y yxyxσσσρ Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 440  The Correlation Coefficient always falls between 1 and +1  = 0 x and y are not linearly related. The farther  is from zero, the stronger the linear relationship:  = +1 x and y have a perfect positive linear relationship  = 1 x and y have a perfect negative linear relationship Interpreting the Correlation Coefficient Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 441 Chapter Summary  Described approaches to assessing probabilities  Developed mon rules of probability  Used Bayes‟ Theorem for conditional probabilities  Distinguished between discrete and continuous probability distributions  Examined discrete probability distributions and their summary measures Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 442 Business Statistics: A DecisionMaking Approach 6th Edition Chapter 5 Discrete and Continuous Probability Distributions Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 443 Chapter Goals After pleting this chapter, you should be able to:  Apply the binomial distribution to applied problems  Compute probabilities for the Poisson and hypergeometric distributions  Find probabilities using a normal distribution table and apply the normal distribution to business problems  Recognize when to apply the uniform and exponential distributions Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 444 Probability Distributions Continuous Probability Distributions Binomial Hypergeometric Poisson Probability Distributions Discrete Probability Distributions Normal Uniform Exponential Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 445  A discrete random variable is a variable that can assume only a countable number of values Many possible outes:  number of plaints per day  number of TV‟s in a household  number of rings before the phone is answered Only two possible outes:  gender: male or female  defective: yes or no  spreads peanut butter first vs. spreads jelly first Discrete Probability Distributions Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 446 Continuous Probability Distributions  A continuous random variable is a variable that can assume any value on a continuum (can assume an uncountable number of values)  thickness of an item  time required to plete a task  temperature of a solution  height, in inches  These can potentially take on any value, depending only on the ability to measure accurately. Business Statistics: A DecisionMaking Approach, 6e 169。 2020 PrenticeHall, Inc. Chap 447 The Binomial Distribution Binomial Hypergeometric Poisson Probability Distrib。