Concept explainers
a.
Find the
a.
Answer to Problem 64CE
The probability of selecting a family that prepared their own taxes is 0.50.
Explanation of Solution
Calculation:
The total number of families is 20 and the number of families prepared their own taxes is 10, the number of families prepared their taxes by a local professional is 7 and the number of families prepared by H&R block is 3.
The probability of selecting a family that prepared their own taxes is obtained as follows:
Thus, the probability of selecting a family that prepared their own taxes is 0.50.
b.
Find the probability that selecting two families, both of which prepared their own taxes.
b.
Answer to Problem 64CE
The probability that selecting two families, both of which prepared their own taxes is 0.2368.
Explanation of Solution
Calculation:
The probability that selecting two families, both of which prepared their own taxes is obtained as follows:
Thus, the probability that selecting two families, both of which prepared their own taxes is 0.2368.
c.
Find the probability of selecting three families, all of which prepared their own taxes.
c.
Answer to Problem 64CE
The probability of selecting three families, all of which prepared their own taxes is 0.1053.
Explanation of Solution
Calculation:
The probability of selecting three families, all of which prepared their own taxes is obtained as follows:
Thus, the probability of selecting three families, all of which prepared their own taxes is 0.1053.
d.
Find the probability that selecting two families, neither of which had their taxes prepared by H&R block.
d.
Answer to Problem 64CE
The probability that selecting two families, neither of which had their taxes prepared by H&R block is 0.7158.
Explanation of Solution
Calculation:
The number of families prepared by H&R block is 3 and the total number of families is 20.
The probability that selecting two families, neither of which had their taxes prepared by H&R block is obtained as follows:
Thus, the probability that selecting two families, neither of which had their taxes prepared by H&R block is 0.7158.
Want to see more full solutions like this?
Chapter 5 Solutions
Loose Leaf for Statistical Techniques in Business and Economics (Mcgraw-hill/Irwin Series in Operations and Decision Sciences)
- 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
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning