Essentials of Statistics Books a la carte Plus NEW MyLab Statistics with Pearson eText - Access Card Package (5th Edition)
5th Edition
ISBN: 9780133892697
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 5.3, Problem 35BSC
On-Time Flights The U.S. Department of Transportation recently reported that 80.5% of U.S. airline flights arrived on time. Find the
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Throughout, A, B, (An, n≥ 1), and (Bn, n≥ 1) are subsets of 2.
1. Show that
AAB (ANB) U (BA) = (AUB) (AB),
Α' Δ Β = Α Δ Β,
{A₁ U A2} A {B₁ U B2) C (A1 A B₁}U{A2 A B2).
16. Show that, if X and Y are independent random variables, such that E|X|< ∞,
and B is an arbitrary Borel set, then
EXI{Y B} = EX P(YE B).
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
Chapter 5 Solutions
Essentials of Statistics Books a la carte Plus NEW MyLab Statistics with Pearson eText - Access Card Package (5th Edition)
Ch. 5.2 - Random Variable Table 5-7 lists probabilities for...Ch. 5.2 - Discrete or Continuous? Is the random variable...Ch. 5.2 - Probability Distribution Does Table 5-7 describe a...Ch. 5.2 - Unusual For 200 births, the probability of exactly...Ch. 5.2 - Identifying Discrete and Continuous Random...Ch. 5.2 - Prob. 6BSCCh. 5.2 - Identifying Probability Distributions. In...Ch. 5.2 - Identifying Probability Distributions. In...Ch. 5.2 - Identifying Probability Distributions. In...Ch. 5.2 - Identifying Probability Distributions. In...
Ch. 5.2 - Identifying Probability Distributions. In...Ch. 5.2 - Identifying Probability Distributions. In...Ch. 5.2 - Happiness In a survey sponsored by Coca-Cola,...Ch. 5.2 - Identifying Probability Distributions. In...Ch. 5.2 - Genetics. In Exercises 15-18, refer to the...Ch. 5.2 - Genetics. In Exercises 15-18, refer to the...Ch. 5.2 - Genetics. In Exercises 15-18, refer to the...Ch. 5.2 - Genetics. In Exercises 15-18, refer to the...Ch. 5.2 - Car Failures. In Exercises 19-22, refer to the...Ch. 5.2 - Car Failures. In Exercises 19-22, refer to the...Ch. 5.2 - Car Failures. In Exercises 19-22, refer to the...Ch. 5.2 - Prob. 22BSCCh. 5.2 - Expected Value for the Texas Pick 3 Game In the...Ch. 5.2 - Expected Value in Maines Pick 4 Game In Maines...Ch. 5.2 - Prob. 25BBCh. 5.2 - Expected Value for Deal or No Deal The television...Ch. 5.3 - Calculating Probabilities Based on a Saint Index...Ch. 5.3 - Consistent Notation If we use the binomial...Ch. 5.3 - Prob. 3BSCCh. 5.3 - Notation of 0+ Using the same survey from Exercise...Ch. 5.3 - Identifying Binomial Distributions. In Exercises...Ch. 5.3 - Identifying Binomial Distributions. In Exercises...Ch. 5.3 - Veggie Survey In an Idaho Potato Commission survey...Ch. 5.3 - Veggie Survey In an Idaho Potato Commission survey...Ch. 5.3 - Surveying Senators The current Senate consists of...Ch. 5.3 - Identifying Binomial Distributions. In Exercises...Ch. 5.3 - Prob. 11BSCCh. 5.3 - Prob. 12BSCCh. 5.3 - Binomial Probability Formula. In Exercises 13 and...Ch. 5.3 - Prob. 14BSCCh. 5.3 - Using the Binomial Probability Table. In Exercises...Ch. 5.3 - Prob. 16BSCCh. 5.3 - Using the Binomial Probability Table. In Exercises...Ch. 5.3 - Prob. 18BSCCh. 5.3 - Prob. 19BSCCh. 5.3 - Using the Binomial Probability Table. In Exercises...Ch. 5.3 - Prob. 21BSCCh. 5.3 - Prob. 22BSCCh. 5.3 - Prob. 23BSCCh. 5.3 - Prob. 24BSCCh. 5.3 - Using Computer Results. In Exercises 2528, refer...Ch. 5.3 - Prob. 26BSCCh. 5.3 - Prob. 27BSCCh. 5.3 - Using Computer Results. In Exercises 2528, refer...Ch. 5.3 - See You Later Based on a Harris Interactive poll,...Ch. 5.3 - Live TV Based on a Comcast survey, there is a 0.8...Ch. 5.3 - Too Young to Tat Based on a Harris poll, among...Ch. 5.3 - Tainted Currency Based on the American Chemical...Ch. 5.3 - Prob. 33BSCCh. 5.3 - Prob. 34BSCCh. 5.3 - On-Time Flights The U.S. Department of...Ch. 5.3 - Prob. 36BSCCh. 5.3 - Nielsen Rating CBS televised a recent Super Bowl...Ch. 5.3 - Overbooking Flights When someone buys a ticket for...Ch. 5.3 - XSORT Method of Gender Selection When testing a...Ch. 5.3 - Prob. 40BSCCh. 5.3 - Prob. 41BSCCh. 5.3 - Prob. 42BSCCh. 5.3 - Acceptance Sampling. Exercises 35 and 36 involve...Ch. 5.3 - Prob. 44BSCCh. 5.3 - Prob. 45BBCh. 5.3 - Prob. 46BBCh. 5.3 - Prob. 47BBCh. 5.3 - Prob. 48BBCh. 5.4 - Prob. 1BSCCh. 5.4 - Prob. 2BSCCh. 5.4 - Prob. 3BSCCh. 5.4 - Prob. 4BSCCh. 5.4 - Finding , , and Unusual Values. In Exercises 58,...Ch. 5.4 - Prob. 6BSCCh. 5.4 - Prob. 7BSCCh. 5.4 - Prob. 8BSCCh. 5.4 - Prob. 9BSCCh. 5.4 - Prob. 10BSCCh. 5.4 - Are 20% of MM Candies Orange? Mars, Inc. claims...Ch. 5.4 - Are 14% of MM Candies Yellow? Mars, Inc. claims...Ch. 5.4 - Cell Phones and Brain Cancer In a study of 420,095...Ch. 5.4 - Prob. 14BSCCh. 5.4 - Prob. 15BSCCh. 5.4 - Prob. 16BSCCh. 5.4 - Prob. 17BSCCh. 5.4 - Prob. 18BSCCh. 5.4 - Born on the 4th of July For the following...Ch. 5.4 - Prob. 20BSCCh. 5.4 - Prob. 21BBCh. 5.4 - Prob. 23BBCh. 5 - Is a probability distribution defined if the only...Ch. 5 - There are 100 questions from an SAT test, and they...Ch. 5 - Using the same SAT questions described in Exercise...Ch. 5 - Prob. 4CQQCh. 5 - If boys and girls are equally likely, groups of400...Ch. 5 - In Exercises 610, use the following: Five American...Ch. 5 - x p(x) 0 0+ 1 0.006 2 0.051 3 0.205 4 0.409 5...Ch. 5 - In Exercises 610, use the following: Five American...Ch. 5 - In Exercises 610, use the following: Five American...Ch. 5 - In Exercises 610, use the following: Five American...Ch. 5 - In Exercises 14, assume that 40% of the population...Ch. 5 - Prob. 2RECh. 5 - Prob. 3RECh. 5 - Brown Eyes When randomly selecting 600 people, the...Ch. 5 - In Exercises 5 and 6, refer to the table in die...Ch. 5 - In Exercises 5 and 6, refer to the table in die...Ch. 5 - Prob. 7RECh. 5 - Prob. 8RECh. 5 - Expected Value for a Magazine Sweepstakes Readers...Ch. 5 - Prob. 10RECh. 5 - Please be aware that some of the following...Ch. 5 - Ohio Pick 4 In Ohios Pick 4 game, you pay 1 to...Ch. 5 - Tennis Challenge In the last U.S. Open tennis...Ch. 5 - Prob. 4CRECh. 5 - Random Digits The digits 0, 1, 2,3,4, 5,6,7, 8,...Ch. 5 - Prob. 6CRECh. 5 - FROM DATA TO DECISION Critical Thinking: Did...
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- Exercise 4.2 Prove that, if A and B are independent, then so are A and B, Ac and B, and A and B.arrow_forward8. Show that, if {Xn, n ≥ 1) are independent random variables, then sup X A) < ∞ for some A.arrow_forward8- 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_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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