Understandable Statistics: Concepts and Methods
12th Edition
ISBN: 9781337119917
Author: Charles Henry Brase, Corrinne Pellillo Brase
Publisher: Cengage Learning
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Chapter 7.3, Problem 23P
(a)
To determine
Find the number of medical files whenthere is no preliminary estimate for p.
(b)
To determine
Find the number of medical files when there is preliminary estimate that about 8 out of 90 people have blood type B.
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Proposition 1.1 Suppose that X1, X2,... are random variables. The following
quantities are random variables:
(a) max{X1, X2) and min(X1, X2);
(b) sup, Xn and inf, Xn;
(c) lim sup∞ X
and lim inf∞ Xn-
(d) If Xn(w) converges for (almost) every w as n→ ∞, then lim-
random variable.
→ Xn is a
Exercise 4.2 Prove that, if A and B are independent, then so are A and B, Ac and
B, and A and B.
8. Show that, if {Xn, n ≥ 1) are independent random variables, then
sup X A) < ∞ for some A.
Chapter 7 Solutions
Understandable Statistics: Concepts and Methods
Ch. 7.1 - In Problems 18, answer true or false. Explain your...Ch. 7.1 - In Problems 18, answer true or false. Explain your...Ch. 7.1 - In Problems 18, answer true or false. Explain your...Ch. 7.1 - In Problems 18, answer true or false. Explain your...Ch. 7.1 - In Problems 18, answer true or false. Explain your...Ch. 7.1 - In Problems 18, answer true or false. Explain your...Ch. 7.1 - In Problems 18, answer true or false. Explain your...Ch. 7.1 - In Problems 18, answer true or false. Explain your...Ch. 7.1 - Critical Thinking Sam computed a 95% confidence...Ch. 7.1 - Critical Thinking Sam computed a 90% confidence...
Ch. 7.1 - Basic Computation: Confidence Interval Suppose x...Ch. 7.1 - Basic Computation: Confidence Interval Suppose x...Ch. 7.1 - Basic Computation: Sample Size Suppose x has a...Ch. 7.1 - Basic Computation: Sample Size Suppose x has a...Ch. 7.1 - Zoology: Hummingbirds Allens hummingbird...Ch. 7.1 - Diagnostic Tests: Uric Acid Overproduction of uric...Ch. 7.1 - Diagnostic Tests: Plasma Volume Total plasma...Ch. 7.1 - Agriculture: Watermelon What price do farmers get...Ch. 7.1 - Prob. 19PCh. 7.1 - Confidence Intervals: Values of A random sample...Ch. 7.1 - Confidence Intervals: Sample Size A random sample...Ch. 7.1 - Ecology: Sand Dunes At wind speeds above 1000...Ch. 7.1 - Prob. 23PCh. 7.1 - Prob. 24PCh. 7.1 - Prob. 25PCh. 7.2 - Use Table 6 of Appendix II to find tc for a 0.95...Ch. 7.2 - Prob. 2PCh. 7.2 - Prob. 3PCh. 7.2 - Prob. 4PCh. 7.2 - Prob. 5PCh. 7.2 - Prob. 6PCh. 7.2 - Prob. 7PCh. 7.2 - Prob. 8PCh. 7.2 - Prob. 9PCh. 7.2 - Prob. 10PCh. 7.2 - Basic Computation: Confidence Interval Suppose x...Ch. 7.2 - Basic Computation: Confidence Interval A random...Ch. 7.2 - In Problems 1319, assume that the population of x...Ch. 7.2 - In Problems 1319, assume that the population of x...Ch. 7.2 - In Problems 1319, assume that the population of x...Ch. 7.2 - In Problems 1319, assume that the population of x...Ch. 7.2 - In Problems 1319, assume that the population of x...Ch. 7.2 - Prob. 18PCh. 7.2 - Prob. 19PCh. 7.2 - Prob. 20PCh. 7.2 - Prob. 21PCh. 7.2 - Prob. 22PCh. 7.2 - Prob. 23PCh. 7.3 - For all these problems, carry at least four digits...Ch. 7.3 - Prob. 2PCh. 7.3 - Prob. 3PCh. 7.3 - Prob. 4PCh. 7.3 - For all these problems, carry at least four digits...Ch. 7.3 - Prob. 6PCh. 7.3 - Prob. 7PCh. 7.3 - Prob. 8PCh. 7.3 - Prob. 9PCh. 7.3 - For all these problems, carry at least four digits...Ch. 7.3 - Prob. 11PCh. 7.3 - Prob. 12PCh. 7.3 - Prob. 13PCh. 7.3 - For all these problems, carry at least four digits...Ch. 7.3 - Prob. 15PCh. 7.3 - Prob. 16PCh. 7.3 - Prob. 17PCh. 7.3 - Prob. 18PCh. 7.3 - Prob. 19PCh. 7.3 - Prob. 20PCh. 7.3 - Prob. 21PCh. 7.3 - Prob. 22PCh. 7.3 - Prob. 23PCh. 7.3 - Prob. 24PCh. 7.3 - Prob. 25PCh. 7.3 - Prob. 26PCh. 7.3 - Prob. 27PCh. 7.3 - Prob. 28PCh. 7.4 - Prob. 1PCh. 7.4 - Prob. 2PCh. 7.4 - Prob. 3PCh. 7.4 - Prob. 4PCh. 7.4 - Prob. 5PCh. 7.4 - Prob. 6PCh. 7.4 - Prob. 7PCh. 7.4 - Prob. 8PCh. 7.4 - Prob. 9PCh. 7.4 - Prob. 10PCh. 7.4 - Prob. 11PCh. 7.4 - Prob. 12PCh. 7.4 - Prob. 13PCh. 7.4 - Prob. 14PCh. 7.4 - Prob. 15PCh. 7.4 - Prob. 16PCh. 7.4 - Answers may vary slightly due to rounding....Ch. 7.4 - Prob. 18PCh. 7.4 - Prob. 19PCh. 7.4 - Prob. 20PCh. 7.4 - Prob. 21PCh. 7.4 - Prob. 22PCh. 7.4 - Prob. 23PCh. 7.4 - Prob. 24PCh. 7.4 - Prob. 25PCh. 7.4 - Prob. 26PCh. 7.4 - Prob. 27PCh. 7.4 - Prob. 28PCh. 7.4 - Prob. 29PCh. 7.4 - Prob. 30PCh. 7.4 - Prob. 31PCh. 7 - Prob. 1CRPCh. 7 - Critical Thinking Suppose you are told that a 95%...Ch. 7 - Prob. 3CRPCh. 7 - Prob. 4CRPCh. 7 - Prob. 5CRPCh. 7 - For Problems 419, categorize each problem...Ch. 7 - Prob. 7CRPCh. 7 - For Problems 419, categorize each problem...Ch. 7 - Prob. 9CRPCh. 7 - For Problems 419, categorize each problem...Ch. 7 - For Problems 419, categorize each problem...Ch. 7 - For Problems 419, categorize each problem...Ch. 7 - Prob. 13CRPCh. 7 - Prob. 14CRPCh. 7 - Prob. 15CRPCh. 7 - For Problems 419, categorize each problem...Ch. 7 - Prob. 17CRPCh. 7 - Prob. 18CRPCh. 7 - Prob. 19CRPCh. 7 - Prob. 1DHCh. 7 - Prob. 2DHCh. 7 - Prob. 3DHCh. 7 - Prob. 1LCCh. 7 - Prob. 2LCCh. 7 - Prob. 3LCCh. 7 - Prob. 1UT
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- 8- 6. Show that, for any random variable, X, and a > 0, 8 心 P(xarrow_forward15. This problem extends Problem 20.6. Let X, Y be random variables with finite mean. Show that 00 (P(X ≤ x ≤ Y) - P(X ≤ x ≤ X))dx = E Y — E X.arrow_forward(b) Define a simple random variable. Provide an example.arrow_forward17. (a) Define the distribution of a random variable X. (b) Define the distribution function of a random variable X. (c) State the properties of a distribution function. (d) Explain the difference between the distribution and the distribution function of X.arrow_forward16. (a) Show that IA(w) is a random variable if and only if A E Farrow_forward15. Let 2 {1, 2,..., 6} and Fo({1, 2, 3, 4), (3, 4, 5, 6}). (a) Is the function X (w) = 21(3, 4) (w)+711.2,5,6) (w) a random variable? Explain. (b) Provide a function from 2 to R that is not a random variable with respect to (N, F). (c) Write the distribution of X. (d) Write and plot the distribution function of X.arrow_forward20. Define the o-field R2. Explain its relation to the o-field R.arrow_forward7. Show that An → A as n→∞ I{An} - → I{A} as n→ ∞.arrow_forward7. (a) Show that if A,, is an increasing sequence of measurable sets with limit A = Un An, then P(A) is an increasing sequence converging to P(A). (b) Repeat the same for a decreasing sequence. (c) Show that the following inequalities hold: P (lim inf An) lim inf P(A) ≤ lim sup P(A) ≤ P(lim sup A). (d) Using the above inequalities, show that if A, A, then P(A) + P(A).arrow_forward19. (a) Define the joint distribution and joint distribution function of a bivariate ran- dom variable. (b) Define its marginal distributions and marginal distribution functions. (c) Explain how to compute the marginal distribution functions from the joint distribution function.arrow_forward18. Define a bivariate random variable. Provide an example.arrow_forward6. (a) Let (, F, P) be a probability space. Explain when a subset of ?? is measurable and why. (b) Define a probability measure. (c) Using the probability axioms, show that if AC B, then P(A) < P(B). (d) Show that P(AUB) + P(A) + P(B) in general. Write down and prove the formula for the probability of the union of two sets.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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