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# Suppose that, as in Exercises 5.11 and 5.79, Y1 and Y2 are uniformly distributed over

Mathematical Statistics with Applications | 7th Edition

Problem 5.95

Suppose that, as in Exercises 5.11 and 5.79, Y1 and Y2 are uniformly distributed over the triangle shaded in the accompanying diagram. (1, 0) (1, 0) (0, 1) y1 y2 a Find Cov(Y1, Y2). b Are Y1 and Y2 independent? (See Exercise 5.55.) c Find the coefficient of correlation for Y1 and Y2. d Does your answer to part (b) lead you to doubt your answer to part (a)? Why or why not?

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Note: Pop. is short for Population Quick review sampling/sample size: the number of observations in a sample. We take a sample from the population. Law of Averages: Averages and proportions vary less from the “expected” as sample size increases;the statistical tendency toward a fixed proportion in the results when an experiment is repeated a large number of times Ex: Toss a coin 100 timespercentage of heads (not the # of heads) gets closer to 50% # of heads = half the # of tosses + chance error  chance error: likely to become larger as # of tosses increases, but likely to be small when compared to the total number of tosses. So, as sample size the precision in predicting from the expected

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Suppose that, as in Exercises 5.11 and 5.79, Y1 and Y2 are uniformly distributed over