Research Methods for the Behavioral Sciences (MindTap Course List)
6th Edition
ISBN: 9781337613316
Author: Frederick J Gravetter, Lori-Ann B. Forzano
Publisher: Cengage Learning
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Chapter 1, Problem 5E
According to the gambler’s fallacy, if a coin toss results in heads three times in a row, then the
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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
Exercise 4.2 Prove that, if A and B are independent, then so are A and B, Ac and
B, and A and B.
Chapter 1 Solutions
Research Methods for the Behavioral Sciences (MindTap Course List)
Ch. 1.1 - Compare and contrast the nonscientific methods for...Ch. 1.2 - Identify and describe the steps of the scientific...Ch. 1.2 - Define induction and deduction and explain the...Ch. 1.2 - Distinguish between a hypothesis and a prediction.Ch. 1.2 - Explain what it means to say that the scientific...Ch. 1.2 - Prob. 6LOCh. 1.3 - Distinguish between qualitative and quantitative...Ch. 1.3 - Identify and describe the steps in the research...Ch. 1 - In addition to the key words that were defined in...Ch. 1 - Describe how some behaviors can be explained by...
Ch. 1 - Describe why you might be cautious about using the...Ch. 1 - Suppose that you are debating whether to hitchhike...Ch. 1 - According to the gamblers fallacy, if a coin toss...Ch. 1 - In this chapter, we identified the method of...Ch. 1 - What are the five steps of the scientific method?Ch. 1 - Describe the difference between inductive and...Ch. 1 - State a hypothesis that identifies a specific...Ch. 1 - Describe what it means to say that science is...Ch. 1 - An expert appears on a shopping network to explain...Ch. 1 - A social science researcher would like to...
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- 8. 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_forward18. Define a bivariate random variable. Provide an example.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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