统计学课件（英文版）ch06.pptVIP

Slides Prepared by JOHN S. LOUCKS St. Edward抯 University Chapter 6 Continuous Probability Distributions Uniform Probability Distribution Normal Probability Distribution Exponential Probability Distribution m x f(x) Continuous Probability Distributions A continuous random variable can assume any value in an interval on the real line or in a collection of intervals. It is not possible to talk about the probability of the random variable assuming a particular value. Instead, we talk about the probability of the random variable assuming a value within a given interval. The probability of the random variable assuming a value within some given interval from x1 to x2 is defined to be the area under the graph of the probability density function between x1 and x2. A random variable is uniformly distributed whenever the probability is proportional to the interval抯 length. Uniform Probability Density Function f(x) = 1/(b - a) for a < x < b = 0 elsewhere where: a = smallest value the variable can assume b = largest value the variable can assume Uniform Probability Distribution Uniform Probability Distribution Expected Value of x E(x) = (a + b)/2 Variance of x Var(x) = (b - a)2/12 where: a = smallest value the variable can assume b = largest value the variable can assume Example: Slater's Buffet Uniform Probability Distribution Slater customers are charged for the amount of salad they take. Sampling suggests that the amount of salad taken is uniformly distributed between 5 ounces and 15 ounces. The probability density function is f(x) = 1/10 for 5 < x < 15 = 0 elsewhere where: x = salad plate filling weight Example: Slater's Buffet Uniform Probability Distribution for Salad Plate Filling Weight f(x) x 5 10 15 1/10 Salad Weight (oz.) Example: Slater's Buffet Uniform Probability Distribution What is the probability that a cust