Recall the example from Section 18.3, where we investigated whether the

software data are exponential by means of the Kolmogorov-Smirnov distance

between the empirical distribution function Fn of the data and the estimated

exponential distribution function:

Tks = sup a?R

|Fn(a) ? (1 ? e??a? )|.

For the data we found tks = 0.176. By means of a new parametric bootstrap

we simulated 100 000 realizations of Tks and found that all of them are smaller

than 0.176. What can you say about the p-value corresponding to 0.176?

25.10 Consider the coal data from Table 23.1, where 23 gross calorific value

measurements are listed for Osterfeld coal coded 262DE27. We modeled this

dataset as a realization of a random sample from a normal distribution with

expectation unknown and standard deviation 0.1 MJ/kg. We are planning

to buy a shipment if the gross calorific value exceeds 23.75 MJ/kg. In order

to decide whether this is sensible, we test the null hypothesis H0 : = 23.75

with test statistic Xn.

a. What would you choose as the alternative hypothesis?

b. For the dataset xn is 23.788. Compute the corresponding p-value, using

that Xn has an N(23.75,(0.1)2/23) distribution under the null hypothesis.

Give an example of two discrete random variables X and Y on the same sample space

such that X and Y have the same distribution, with support {1, 2,..., 10}, but the

event X = Y never occurs. If X and Y are independent, is it still possible to construct

such an example?

40. Suppose X and Y are discrete r.v.s such that P(X = Y ) = 1. This means that X and

Y always take on the same value.

(a) Do X and Y have the same PMF?

(b) Is it possible for X and Y to be independent?

41. If X, Y, Z are r.v.s such that X and Y are independent and Y and Z are independent,

does it follow that X and Z are independent

19. Suppose that the miles-per-gallon (mpg) rating of passenger cars is a normally distributed random variable with a mean and a standard deviation of 33.8 and 3.5 mpg, respectively. a. What is the probability that a randomly selected passenger car gets more than 35 mpg? b. What is the probability that the average mpg of four randomly selected passenger cars is more than 35 mpg? c. If four passenger cars are randomly selected, what is the probability that all of the passenger cars get more than 35 mpg?BRINGING IT ALL TOGETHER Chapter 6 Case Study: SAT Scores and AP Exam Scores. The table contains the frequency CASE STUDY distribution of X = score on the Statistics Advanced Placement Exam for students from California. Use this information for Exercises 78-88. APstats X = Statistics AP exam score Frequency 3,464 5,108 - NWAI 6,333 4,937 6,058 Total N = 25,900But MyEagle Bed Assignments: 6211-DUS-2905-Business Statistics-RT-27750 Chapter 6 Assignment 7 Exercise 6-31 (Algo) (LO6-6) In a Poisson distribution, points # = 3.10 . (Round your answers to 4 decimal places.) a. What is the probability that x= 1? Book Probablyty Print References b. What is the probability that X307 Probability 17 A 2 3 A 6 Q W E R T Y U78. Explain why the Statistics AP exam score is a random variable. 79. Explain why the Statistics AP exam score is a discrete, not a continuous, variable. 80. Construct the probability distribution table for X = Statistics AP exam score. 81. Confirm that your probability distribution in Exercise 8( is valid. 82. Draw a probability distribution graph of X. 83. Calculate the following probabilities: a. P(X > 2) b. P(X > 1) c. P(X = 2) d. P(X