PROBABILITY AND STATISTICS FOR ENGINEER
9th Edition
ISBN: 2818000048605
Author: WALPOLE
Publisher: PEARSON
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Chapter 3.4, Problem 67RE
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Question 3
The following stem-and-leaf displays the weekly salary of employees at this firm.
Stem-and-Leaf Display
Leaf Unit = 10.0
N=x
5
3 00123
12 4 0125888
(y)
5 11234456777
z
6 13568
5
7 154
2
8 46
i.
Determine the value of x, y and z.
[3]
ii. What is the value of the median?
[2]
iii.
Find the mode of this data set.
iv.
Calculate the range
[1]
[2]
Let Y be a continuous RV with PDF
otherwise
Find the CDF, Fry), of Y .
Find an expression for pth, p € (0, 1), quantile of the distribution.
Find E(Y) and V(Y).
Find E(-2Y + 1) and V(-3Y - 2).
Find E(Y3).
Let X be a continuous RV with CDF
Find P(X < 0), P(-1 < X < 1) and P(0.5 < X).
Based on your answers to the above questions, what is the median of the distribu-tion? Why
Find the PDF, fx (x), of X.
Chapter 3 Solutions
PROBABILITY AND STATISTICS FOR ENGINEER
Ch. 3.3 - Classify the following random variables as...Ch. 3.3 - An overseas shipment of 5 foreign automobiles...Ch. 3.3 - Let W be a random variable giving the number of...Ch. 3.3 - A coin is flipped until 3 heads in succession...Ch. 3.3 - Determine the value c so that each of the...Ch. 3.3 - Prob. 6ECh. 3.3 - The total number of hours, measured in units of100...Ch. 3.3 - Find the probability distribution of the random...Ch. 3.3 - Prob. 9ECh. 3.3 - Find a formula for the probability distribution of...
Ch. 3.3 - A shipment of 7 television sets contains 2...Ch. 3.3 - An investment firm offers its customers municipal...Ch. 3.3 - The probability distribution of X, the number of...Ch. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Construct a graph of the cumulative distribution...Ch. 3.3 - A continuous random variable X that can assume...Ch. 3.3 - A continuous random variable X that can assume...Ch. 3.3 - For the density function of Exercise 3.17, find...Ch. 3.3 - For the density function of Exercise 3.18, find...Ch. 3.3 - Consider the density function
Evaluate k.
Find...Ch. 3.3 - Three cards are drawn in succession from a deck...Ch. 3.3 - Prob. 23ECh. 3.3 - Find the probability distribution for the number...Ch. 3.3 - From a box containing 4 dimes and 2 nickels, 3...Ch. 3.3 - From a box containing 4 black balls and 2 green...Ch. 3.3 - The time to failure in hours of an important piece...Ch. 3.3 - Prob. 28ECh. 3.3 - Prob. 29ECh. 3.3 - Measurements of scientific systems are always...Ch. 3.3 - Based on extensive testing, it is determined by...Ch. 3.3 - Prob. 32ECh. 3.3 - Suppose a certain type of small data processing...Ch. 3.3 - Magnetron tubes are produced on an automated...Ch. 3.3 - Suppose it is known from large amounts of...Ch. 3.3 - On a laboratory assignment, if the equipment is...Ch. 3.4 - Prob. 37ECh. 3.4 - If the joint probability distribution of X and Y...Ch. 3.4 - Prob. 39ECh. 3.4 - Prob. 40ECh. 3.4 - Prob. 41ECh. 3.4 - Let X and Y denote the lengths of life, in years,...Ch. 3.4 - Prob. 43ECh. 3.4 - Prob. 44ECh. 3.4 - Let X denote the diameter of an armored electric...Ch. 3.4 - Referring to Exercise 3.38, find
the marginal...Ch. 3.4 - The amount of kerosene, in thousands of liters, in...Ch. 3.4 - Referring to Exercise 3.39, find
f(y|2) for all...Ch. 3.4 - Let X denote the number of times a certain...Ch. 3.4 - Suppose that X and Y have the following joint...Ch. 3.4 - Prob. 51ECh. 3.4 - A coin is tossed twice. Let Z denote the number of...Ch. 3.4 - Given the joint density function
find P(1< Y < 3...Ch. 3.4 - Determine whether the two random variables of...Ch. 3.4 - Determine whether the two random variables of...Ch. 3.4 - The joint density function of the random variables...Ch. 3.4 - Let X, Y, and Z have the joint probability density...Ch. 3.4 - Determine whether the two random variables of...Ch. 3.4 - Prob. 59ECh. 3.4 - The joint probability density function of the...Ch. 3.4 - Prob. 61RECh. 3.4 - Prob. 62RECh. 3.4 - Prob. 63RECh. 3.4 - Prob. 64RECh. 3.4 - Prob. 65RECh. 3.4 - Prob. 66RECh. 3.4 - Prob. 67RECh. 3.4 - Prob. 68RECh. 3.4 - Prob. 69RECh. 3.4 - Prob. 70RECh. 3.4 - Prob. 71RECh. 3.4 - Prob. 72RECh. 3.4 - Prob. 73RECh. 3.4 - Prob. 74RECh. 3.4 - A chemical system that results from a chemical...Ch. 3.4 - Consider the situation of Review Exercise 3.75....Ch. 3.4 - Prob. 77RECh. 3.4 - Prob. 78RECh. 3.4 - Prob. 79RECh. 3.4 - Prob. 80RE
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- A survey of 581 citizens found that 313 of them favor a new bill introduced by the city. We want to find a 95% confidence interval for the true proportion of the population who favor the bill. What is the lower limit of the interval? Enter the result as a decimal rounded to 3 decimal digits. Your Answer:arrow_forwardLet X be a continuous RV with PDF where a > 0 and 0 > 0 are parameters. verify that f-∞ /x (x)dx = 1. Find the CDF, Fx (7), of X.arrow_forward6. [20] Let X be a continuous RV with PDF 2(1), 1≤x≤2 fx(x) = 0, otherwisearrow_forward
- A survey of 581 citizens found that 313 of them favor a new bill introduced by the city. We want to find a 95% confidence interval for the true proportion of the population who favor the bill. What is the lower limit of the interval? Enter the result as a decimal rounded to 3 decimal digits. Your Answer:arrow_forwardA survey of 581 citizens found that 313 of them favor a new bill introduced by the city. We want to find a 95% confidence interval for the true proportion of the population who favor the bill. What is the lower limit of the interval? Enter the result as a decimal rounded to 3 decimal digits. Your Answer:arrow_forward2. The SMSA data consisting of 141 observations on 10 variables is fitted by the model below: 1 y = Bo+B1x4 + ẞ2x6 + ẞ3x8 + √1X4X8 + V2X6X8 + €. See Question 2, Tutorial 3 for the meaning of the variables in the above model. The following results are obtained: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.302e+03 4.320e+02 3.015 0.00307 x4 x6 x8 x4:x8 x6:x8 -1.442e+02 2.056e+01 -7.013 1.02e-10 6.340e-01 6.099e+00 0.104 0.91737 -9.455e-02 5.802e-02 -1.630 0.10550 2.882e-02 2.589e-03 11.132 1.673e-03 7.215e-04 2.319 F) x4 1 3486722 3486722 17.9286 4.214e-05 x6 1 14595537 x8 x4:x8 x6:x8 1 132.4836 < 2.2e-16 1045693 194478 5.3769 0.02191 1 1198603043 1198603043 6163.1900 < 2.2e-16 1 25765100 25765100 1045693 Residuals 135 26254490 Estimated variance matrix (Intercept) x4 x6 x8 x4:x8 x6:x8 (Intercept) x4 x6 x8 x4:x8 x6:x8 0.18875694 1.866030e+05 -5.931735e+03 -2.322825e+03 -16.25142055 0.57188953 -5.931735e+03 4.228816e+02 3.160915e+01 0.61621781 -0.03608028 -0.00445013 -2.322825e+03…arrow_forward
- In some applications the distribution of a discrete RV, X resembles the Poisson distribution except that 0 is not a possible value of X. Consider such a RV with PMF where 1 > 0 is a parameter, and c is a constant. (a) Find the expression of c in terms of 1. (b) Find E(X). (Hint: You can use the fact that, if Y ~ Poisson(1), the E(Y) = 1.)arrow_forwardSuppose that X ~Bin(n,p). Show that E[(1 - p)] = (1-p²)".arrow_forwardI need help with this problem and an explanation of the solution for the image described below. (Statistics: Engineering Probabilities)arrow_forward
- I need help with this problem and an explanation of the solution for the image described below. (Statistics: Engineering Probabilities)arrow_forwardThis exercise is based on the following data on four bodybuilding supplements. (Figures shown correspond to a single serving.) Creatine(grams) L-Glutamine(grams) BCAAs(grams) Cost($) Xtend(SciVation) 0 2.5 7 1.00 Gainz(MP Hardcore) 2 3 6 1.10 Strongevity(Bill Phillips) 2.5 1 0 1.20 Muscle Physique(EAS) 2 2 0 1.00 Your personal trainer suggests that you supplement with at least 10 grams of creatine, 39 grams of L-glutamine, and 90 grams of BCAAs each week. You are thinking of combining Xtend and Gainz to provide you with the required nutrients. How many servings of each should you combine to obtain a week's supply that meets your trainer's specifications at the least cost? (If an answer does not exist, enter DNE.) servings of xtend servings of gainzarrow_forwardI need help with this problem and an explanation of the solution for the image described below. (Statistics: Engineering Probabilities)arrow_forward
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