概率统计(英文) chapter5 Joint Probability Distributions and Random Samples.ppt

Example 5.27 A certain consumer organization customarily reports the number of major defects for each new automobile that it tests. Suppose the number of such defects for a certain model is a random variable with mean value 3.2 and standard deviation 2.4. Among 100 randomly selected cars of this model, how likely is it that the sample average number of major defects exceeds 4? Solution : Let Xi denote the number of major defects for the ith car in the random sample. Notice that Xi is a discrete rv, but the CLT is applicable whether the variable of interest is discrete or continuous. Also, although the fact that the standard deviation of this nonnegative variable is quite large relative to the mean value suggest that its distribution is positively skew, the large sample size implies that X does have approximately a normal distribution. Using and The CLT provides insight into why many random variables have probability distributions that are approximately normal. For example, the measurement error in a scientific experiment can be thought of as the sum of a number of underlying perturbations and errors of small magnitude. Rule of thumb: If n30, the Central Limit Theorem can be used Exercise P238 48 Let X1, X2, …,X100 denote the actual net weights of 100 randomly selected 50-lb bags of fertilizer. If the expected weight of each bag is 50 and the variance is 1, calculate (approximately) using the CLT? If the expected weight is 49.8 lb rather than 50 lb so that on average bags are underfilled, calculate Exercise P239 52 The lifetime of a certain type of battery is normally distributed with mean value 10 hours and standard deviation 1 hour. There are four batteries in a package. What lifetime value such that the total lifetime of all batteries in a package exceeds that value for only 5% of all packages? The mid-term Examination in 2007 1.(15’)Let be a random variable with the following probability distr