Introduction to Business Statistics
7th Edition
ISBN: 9781111792374
Author: WEIERS
Publisher: Cengage Learning
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Chapter 6.1, Problem 6.1E
To determine
To explain:
The reason for mentioning random variable as "random".
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3. [15] The joint PDF of RVS X and Y is given by
fx.x(x,y) = {
x) = { c(x +
{
c(x+y³),
0,
0≤x≤ 1,0≤ y ≤1
otherwise
where c is a constant.
(a) Find the value of c.
(b) Find P(0 ≤ X ≤,
Need help please
7. [10] Suppose that Xi, i = 1,..., 5, are independent normal random variables, where
X1, X2 and X3 have the same distribution N(1, 2) and X4 and X5 have the same
distribution N(-1, 1). Let
(a) Find V(X5 - X3).
1
= √(x1 + x2) — — (Xx3 + x4 + X5).
(b) Find the distribution of Y.
(c) Find Cov(X2 - X1, Y).
-
Chapter 6 Solutions
Introduction to Business Statistics
Ch. 6.1 - Prob. 6.1ECh. 6.1 - Indicate whether each of the following random...Ch. 6.1 - Indicate whether each of the following random...Ch. 6.1 - Prob. 6.4ECh. 6.1 - Prob. 6.5ECh. 6.1 - Determine the mean, variance, and standard...Ch. 6.1 - Determine the mean, variance, and standard...Ch. 6.1 - Prob. 6.8ECh. 6.1 - Prob. 6.9ECh. 6.1 - Prob. 6.10E
Ch. 6.1 - A consultant has presented his client with three...Ch. 6.1 - Prob. 6.12ECh. 6.1 - Prob. 6.13ECh. 6.1 - Laura McCarthy, the owner of Riverside Bakery, has...Ch. 6.1 - In 2007, nearly 24 million tons of steel mill...Ch. 6.2 - What is necessary for a process to be considered a...Ch. 6.2 - When we are sampling without replacement, under...Ch. 6.2 - Prob. 6.18ECh. 6.2 - Prob. 6.19ECh. 6.2 - A city law-enforcement official has stated that...Ch. 6.2 - Prob. 6.21ECh. 6.2 - According to the National Marine Manufacturers...Ch. 6.2 - In the town of Hickoryville, an adult citizen has...Ch. 6.2 - It has been reported that the overall graduation...Ch. 6.2 - Prob. 6.25ECh. 6.2 - The U.S. Department of Labor has reported that 30%...Ch. 6.2 - Alicia’s schedule includes three Tuesday/Thursday...Ch. 6.2 - OfficeQuip is a small office supply firm that is...Ch. 6.2 - Four wheel bearings are to be replaced on a...Ch. 6.2 - It has been estimated that one in five Americans...Ch. 6.2 - Airlines book more seats than arc actually...Ch. 6.2 - Every day, artists at Arnold’s House of Fine...Ch. 6.3 - Under what circumstances should the hypergeometric...Ch. 6.3 - Using the hypergeometric distribution, with...Ch. 6.3 - Using the hypergeometric distribution, with...Ch. 6.3 - In a criminal trial, there are 25 persons who have...Ch. 6.3 - A computer firm must send a group of three...Ch. 6.3 - Prob. 6.38ECh. 6.4 - Prob. 6.39ECh. 6.4 - Prob. 6.40ECh. 6.4 - Prob. 6.41ECh. 6.4 - Prob. 6.42ECh. 6.4 - The U.S. divorce rate has been reported as 3.6...Ch. 6.4 - During the 12 P.M.-1 P.M. noon hour, arrivals at a...Ch. 6.4 - During the winter heating season in a northern...Ch. 6.4 - Prob. 6.46ECh. 6.4 - Prob. 6.47ECh. 6.4 - Prob. 6.48ECh. 6.4 - Prob. 6.49ECh. 6.4 - A manufacturing plant’s main production line...Ch. 6.4 - Prob. 6.51ECh. 6 - The owner of a charter fishing boat has found that...Ch. 6 - Prob. 6.55CECh. 6 - Prob. 6.56CECh. 6 - Prob. 6.57CECh. 6 - Prob. 6.58CECh. 6 - Prob. 6.59CECh. 6 - Prob. 6.60CECh. 6 - A mining company finds that daily lost-work...Ch. 6 - Prob. 6.62CECh. 6 - Prob. 6.63CECh. 6 - Prob. 6.64CECh. 6 - Prob. 6.65CECh. 6 - Seven of the 15 campus police officers available...Ch. 6 - Prob. 6.67CECh. 6 - Prob. 6.68CECh. 6 - Prob. 6.69CECh. 6 - Prob. 6.70CECh. 6 - Prob. 6.71CECh. 6 - Prob. 6.72CECh. 6 - Prob. 6.73CECh. 6 - Prob. 6.74CECh. 6 - Prob. 6.75CECh. 6 - Prob. 6.76CECh. 6 - Prob. 6.77CECh. 6 - Prob. 6.78CECh. 6 - Prob. 6.79CECh. 6 - Prob. 6.80CE
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- 1. [10] Suppose that X ~N(-2, 4). Let Y = 3X-1. (a) Find the distribution of Y. Show your work. (b) Find P(-8< Y < 15) by using the CDF, (2), of the standard normal distribu- tion. (c) Find the 0.05th right-tail percentage point (i.e., the 0.95th quantile) of the distri- bution of Y.arrow_forward6. [10] Let X, Y and Z be random variables. Suppose that E(X) = E(Y) = 1, E(Z) = 2, V(X) = 1, V(Y) = V(Z) = 4, Cov(X,Y) = -1, Cov(X, Z) = 0.5, and Cov(Y, Z) = -2. 2 (a) Find V(XY+2Z). (b) Find Cov(-x+2Y+Z, -Y-2Z).arrow_forward1. [10] Suppose that X ~N(-2, 4). Let Y = 3X-1. (a) Find the distribution of Y. Show your work. (b) Find P(-8< Y < 15) by using the CDF, (2), of the standard normal distribu- tion. (c) Find the 0.05th right-tail percentage point (i.e., the 0.95th quantile) of the distri- bution of Y.arrow_forward
- == 4. [10] Let X be a RV. Suppose that E[X(X-1)] = 3 and E(X) = 2. (a) Find E[(4-2X)²]. (b) Find V(-3x+1).arrow_forward2. [15] Let X and Y be two discrete RVs whose joint PMF is given by the following table: y Px,y(x, y) -1 1 3 0 0.1 0.04 0.02 I 2 0.08 0.2 0.06 4 0.06 0.14 0.30 (a) Find P(X ≥ 2, Y < 1). (b) Find P(X ≤Y - 1). (c) Find the marginal PMFs of X and Y. (d) Are X and Y independent? Explain (e) Find E(XY) and Cov(X, Y).arrow_forward32. Consider a normally distributed population with mean μ = 80 and standard deviation σ = 14. a. Construct the centerline and the upper and lower control limits for the chart if samples of size 5 are used. b. Repeat the analysis with samples of size 10. 2080 101 c. Discuss the effect of the sample size on the control limits.arrow_forward
- Consider the following hypothesis test. The following results are for two independent samples taken from the two populations. Sample 1 Sample 2 n 1 = 80 n 2 = 70 x 1 = 104 x 2 = 106 σ 1 = 8.4 σ 2 = 7.6 What is the value of the test statistic? If required enter negative values as negative numbers (to 2 decimals). What is the p-value (to 4 decimals)? Use z-table. With = .05, what is your hypothesis testing conclusion?arrow_forwardPeriodically, Merrill Lynch customers are asked to evaluate Merrill Lynch financial consultants and services (2000 Merrill Lynch Client Satisfaction Survey). Higher ratings on the client satisfaction survey indicate better service with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. Use = .05 and test to see whether the consultant with more experience has the higher population mean service rating. Consultant A Consultant B = 16 = 10 = 6.82 = 6.25 = .64 = .75 State the null and alternative hypotheses.H0: 1 - 2 Ha: 1 - 2 Compute the value of the test statistic (to 2 decimals). What is the p-value?The p-value is What is your conclusion?arrow_forwardA firm paid its first annual dividend yesterday in the amount of $.15 per share. The company plans to double the dividend in each of the next 3 years. Starting in Year 4, the firm plans to pay $1.50 per share indefinitely. What is one share of this stock worth today if the market rate of return on similar securities is 13.8 percent? Multiple Choice $11.79 $8.92 $10.77 $11.02 $10.26arrow_forward
- Suppose the random variable X is normally distributed with mean 80 and standard deviation 16. Find following probabilities. Find ‘b’ such that P(X ≥ b) = 0.975. Find the probability using a normal distribution table AND using ti-83 calculator. SHOW ALL STEPS PLEASE.arrow_forwardSuppose the random variable X is normally distributed with mean 80 and standard deviation 16. Find following probabilities. Equation: P(85 ≤ X ≤ 102). Find the probability using a normal distribution table AND using ti-83 calculator. SHOW ALL STEPS PLEASE.arrow_forwardData set is Bachelor Degree's Conferred by Race and Ethnicity.arrow_forward
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