Intro Stats
4th Edition
ISBN: 9780321826275
Author: Richard D. De Veaux
Publisher: PEARSON
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Textbook Question
Chapter 12, Problem 10E
Sample spaces II For each of the following, list the
- a) Roll two dice; record the sum of the numbers.
- b) A family has 3 children; record each child’s sex in order of birth.
- c) Toss four coins; record the number of tails.
- d) Toss a coin 10 times; record the length of the longest run of heads.
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2. Which of the following statements are (not) true?
lim sup{An U Bn}
818
lim sup{A, B}
818
lim inf{An U Bn}
818
818
lim inf{A, B}
An
An A, Bn-
A, BnB
→B
=
=
=
lim sup A, U lim sup Bn;
818
818
lim sup A, lim sup Bn;
818
81U
lim inf A, U lim inf Bn;
818
818
lim inf A, lim inf Bn;
n→X
818
An U BRAUB
as no;
An OBRANB as n→∞.
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).
Chapter 12 Solutions
Intro Stats
Ch. 12.1 - One common proposal for beating the lottery is to...Ch. 12.3 - Prob. 2JCCh. 12 - Flipping a coin Flipping a fair coin is said to...Ch. 12 - Dice Rolling a fair six-sided die is supposed to...Ch. 12 - Flipping a coin II Your friend says: I flipped...Ch. 12 - Dice II After rolling doubles on a pair of dice...Ch. 12 - Wardrobe In your dresser are five blue shirts,...Ch. 12 - Prob. 6ECh. 12 - Prob. 7ECh. 12 - Prob. 8E
Ch. 12 - Sample spaces For each of the following, list the...Ch. 12 - Sample spaces II For each of the following, list...Ch. 12 - Prob. 11ECh. 12 - Rain The weather reporter on TV makes predictions...Ch. 12 - Winter Comment on the following quotation: What I...Ch. 12 - Snow After an unusually dry autumn, a radio...Ch. 12 - Prob. 15ECh. 12 - Prob. 16ECh. 12 - Auto insurance Insurance companies collect annual...Ch. 12 - Prob. 18ECh. 12 - Prob. 19ECh. 12 - Prob. 20ECh. 12 - Electronics Suppose that 46% of families living in...Ch. 12 - Homes Funding for many schools comes from taxes...Ch. 12 - Prob. 23ECh. 12 - Lefties Although its hard to be definitive in...Ch. 12 - Prob. 25ECh. 12 - Prob. 26ECh. 12 - Car repairs A consumer organization estimates that...Ch. 12 - Stats projects In a large Introductory statistics...Ch. 12 - Prob. 29ECh. 12 - Prob. 30ECh. 12 - Prob. 31ECh. 12 - Prob. 32ECh. 12 - 33. Energy 2011 A Gallup Poll in March 2011 asked...Ch. 12 - Prob. 34ECh. 12 - Prob. 35ECh. 12 - Prob. 36ECh. 12 - Prob. 37ECh. 12 - Prob. 38ECh. 12 - Prob. 39ECh. 12 - Blood The American Red Cross says that about 45%...Ch. 12 - Prob. 41ECh. 12 - Prob. 42ECh. 12 - Prob. 43ECh. 12 - Prob. 44ECh. 12 - Prob. 45ECh. 12 - The train To get to work, a commuter must cross...Ch. 12 - Prob. 47ECh. 12 - 48. Religion Census reports for a city indicate...Ch. 12 - Prob. 49ECh. 12 - Pepsi For a sales promotion, the manufacturer...Ch. 12 - 9/11? On September 11, 2002, the first anniversary...Ch. 12 - Prob. 52E
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- 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 aarrow_forwardExercise 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_forward
- 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_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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