离散概率分布.ppt

5-1Chapter 5Discrete DistributionsBusiness Statistics 5-2Chapter pleting this chapter, you should be able to:?Interpret the mean and standard deviation for a discrete probability distribution?Use the binomial probability distribution to find probabilities?Describe when to apply the binomial distribution 5-3Introduction to Probability Distributions?Random Variable?Represents a possible numerical value from an uncertain eventRandom VariablesDiscrete Random VariableContinuousRandom VariableCh. 5Ch. 6 5-4Discrete Random Variables?Can only assume a countable number of valuesExamples: ?Roll a die twiceLet X be the number of times es up (then X could be 0, 1, or 2 times)?Toss a coin 5 times. Let X be the number of heads (then X = 0, 1, 2, 3, 4, or 5) 5-5Probability Distribution for a Discrete Random Variable?A probability distribution (or probability mass function )(pdf) for a discrete random variable is a mutually exclusive listing of all possible numerical es for that random variable such that a particular probability of occurrence is associated with each e. 5-6Experiment: Toss 2 Coins. Let X = # Probability Distribution4 possible esTTHHHHProbability DistributionX ValueProbability 0 1/4 = .25 1 2/4 = .50 2 1/4 = .25 5-7 5-8Discrete Random Variable Summary Measures?Expected Value (or mean) of a discrete distribution (Weighted Average)?Example: Toss 2 coins, X = # of heads, compute expected value of X:E(X) = (0 x .25) + (1 x .50) + (2 x .25) = P(X) 0 .25 1 .50 2 .25?????N1iii)X(PXE(X) 5-9?Variance of a discrete random variable?Standard Deviation of a discrete random variablewhere:E(X) = Expected value of the discrete random variable X Xi = the ith e of XP(Xi) = Probability of the ith occurrence of XDiscrete Random Variable Summary Measures????N1i