[QAStatistics统计学281课堂讲义.ppt

Chapter 6 Continuous Probability Distributions The Uniform Probability Distribution The Normal Probability Distribution Normal Approximation of Binomial Probabilities (Not covered in textbook) The Exponential Probability Distribution Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Continuous Probability Distributions A continuous random variable can assume _________ in an _________ 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.(It is zero) Instead, we talk about the probability of the random variable assuming a value within a given _________. The probability of the random variable assuming a value within some given interval from x1 to x2 is defined to be the ____ under the graph of the probability density function between ___ and___ . Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd. The Uniform Probability Distribution A random variable is uniformly distributed whenever the probability is _________ to the length of the interval. Graph: Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd. The Uniform Probability Distribution Uniform Probability Density Function f (x) = 1/(b - a) for a x b = 0 elsewhere 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 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Example: Slaters Buffet 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. Probability Density Function f (x ) = ________ for 5 x 15 = __