The number of people who visit the Leftorium store in a day is Pois(100). Suppose that

10% of customers are sinister (left-handed), and 90% are dexterous (right-handed). Half

of the sinister customers make purchases, but only a third of the dexterous customers

make purchases. The characteristics and behavior of people are independent, with probabilities as described in the previous two sentences. On a certain day, there are 42 people

who arrive at the store but leave without making a purchase. Given this information,

what is the conditional PMF of the number of customers on that day who make a

purchase?

62. A chicken lays n eggs. Each egg independently does or doesn't hatch, with probability p

of hatching. For each egg that hatches, the chick does or doesn't survive (independently

of the other eggs), with probability s of survival. Let N ? Bin(n, p) be the number of

eggs which hatch, X be the number of chicks which survive, and Y be the number of

chicks which hatch but don't survive (so X + Y = N). Find the marginal PMF of X,

and the joint PMF of X and Y . Are X and Y independent X.

State whether each of the following is true or false.

a. Graphs, tables, and summary statistics all illustrate the application of inferential statistics.

b. Inferential statistics are procedures used to

make inferences about a population, given

only a limited amount of data.

c. Descriptive statistics can be used to describe

populations and samples of data.

13. A researcher measured behavior among all individuals in some small population. Are inferential

statistics necessary to draw conclusions concerning this population? Explain.

14. Appropriately use the terms sample and population to describe the following statement: A statistics class has 25 students enrolled, but only 23

students attended class.

15. On occasion, samples can be larger than the population from which it was selected. Explain why

this can't be true.

16. A researcher demonstrates that eating breakfast in

the morning causes increased alertness throughout the day. What research design must the

researcher have used in this example? Explain.

17. A researcher measures the height and income of

participants and finds that taller men tend to

earn greater incomes than shorter men. What

type of research method did the researcher use in

this example? Explain.

11. Consider the following Balance of Payments data for Borduria. (all in $ billion) Import of Services 25 Export of Goods 55 Inward Remittances 10 Returns to Foreigners for their holding of Financial Assets 15 Export of Services X Foreigners' purchase of domestic property 5 Import of Goods 45 Returns to Domestic Holders of Foreign Financial Assets 10 Domestic purchases of Foreign Property 3 Domestic purchases of Foreign Financial Assets 14 Foreign Purchases of Domestic Financial Statistical Discrepancy 0 Assets 8 Net Addition/Subtraction of Foreign Reserves Y Using the data above, carefully calculate X and Y, showing all steps in the calculations of X and Y. (4) 168 CHAPTER 6 6.36 The method of instruction in college and university Number applied statistics courses is changing. Historically, Drinks most courses were taught with an emphasis on None manual calculation. The alternative is to employ a One computer and a software package to perform the Two calculations. An analysis of applied statistics courses More investigated whether the instructor's educational background is primarily mathematics (or statistics) a. V or some other field. The result of this analysis is the b. accompanying table of joint probabilities. C. Statistics Course Statistics Emphasizes Course d. Education of Manual Computer and Instructor Calculations Software Mathematics or 6.39 statistics education .23 .36 Other education .11 .30 a. What is the probability that a randomly selected applied statistics course instructor whose education was in statistics emphasizes manual calculations? b. What proportion of applied statistics courses Reaso employs a computer and software? Plant c. Are the educational background of the instruc- clo tor and the way his or her course is taught independent? Insu Posi 6.37 A restaurant chain routinely surveys its omers al2. Let X1,...,X ~i.i.d. Exp{). a. Find a consistent estimator for the second moment E(X2) (Hint: Weak Law of Large Numbers). Use the 1;;ng of X to prove that your estimator is consistent in the case a=1, =2. 13. Use the Central Limit Theorem to find the limiting distribution of an appropriately normalized version of your statistic. c. Find the pdf ofm