EBK FIRST COURSE IN PROBABILITY, A
10th Edition
ISBN: 9780134753676
Author: Ross
Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 5, Problem 5.44P
Let Y be a log normal random variable (see Example 7e for its definition) and let
a. cY is lognormal;
b.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Assume that X and Y are two random variables. Suppose Y is exponential with mean 798.
Suppose that, when X is conditional on Y = y, it is exponential with mean y. (X itself is not
exponential, but when X is conditional on Y = y it is exponential.) What is the correlation of X
and Y? Give four decimal places and use random variables.
Listed below are the numbers of deaths resulting from motor vehicle crashes. Let x represent the year, with 1975 coded as x = 1, 1980 coded as x = 6, 1985 coded as
x = 11, and so on. Construct a scatterplot and identify the mathematical model that best fits the given data. Use the best model to find the projected number of deaths for
the year 2028.
x (year)
1975 1980 1985 1990 1995 2000 2005 2010 D
y (deaths) 44,533 51,122 43,809 44,590 41,798 41,960 43,436 32,697
(...)
Choose the correct graph below.
O A.
O B.
O C.
D.
52000-
52000-
52000-
52000-
DDDD
00
X
X
X
X
32000+
32000
32000+
32000+
0
40
0
40
0
40
0
40
What is the equation of the best model? Select the correct choice below and fill in the answer boxes to complete your choice. Enter only nonzero values.
(Type integers or decimals rounded to three decimal places as needed.)
O A.
y= X
B.
y =
+
In x
O C.
y =
+
O D.
X
y=²
O E.
y =
x² +
X +
Use the best model to find the projected number of such deaths for the year 2028.
The projected…
Show that E [ X – m]3 = E(X)3 - 3m, o? - m? where m, and o are the mean and
variance of X respectively.
Chapter 5 Solutions
EBK FIRST COURSE IN PROBABILITY, A
Ch. 5 - Let X be a random variable with probability...Ch. 5 - Prob. 5.2PCh. 5 - Prob. 5.3PCh. 5 - The probability density function of X. the...Ch. 5 - Prob. 5.5PCh. 5 - Compute E[X] if X has a density function given by...Ch. 5 - The density function of X is given by...Ch. 5 - The lifetime in hours of an electronic tube is a...Ch. 5 - Consider Example 4b &I of Chapter 4 &I, but now...Ch. 5 - Trains headed for destination A arrive at the...
Ch. 5 - A point is chosen at random on a line segment of...Ch. 5 - A bus travels between the two cities A and B....Ch. 5 - You arrive at a bus stop at 10A.M., knowing that...Ch. 5 - Let X be a uniform (0, 1) random variable. Compute...Ch. 5 - If X is a normal random variable with parameters...Ch. 5 - The annual rainfall (in inches) in a certain...Ch. 5 - The salaries of physicians in a certain speciality...Ch. 5 - Suppose that X is a normal random variable with...Ch. 5 - Let be a normal random variable with mean 12 and...Ch. 5 - If 65 percent of the population of a large...Ch. 5 - Suppose that the height, in inches, of a...Ch. 5 - Every day Jo practices her tennis serve by...Ch. 5 - One thousand independent rolls of a fair die will...Ch. 5 - The lifetimes of interactive computer chips...Ch. 5 - Each item produced by a certain manufacturer is,...Ch. 5 - Two types of coins are produced at a factory: a...Ch. 5 - In 10,000 independent tosses of a coin, the coin...Ch. 5 - Twelve percent of the population is left handed....Ch. 5 - A model for the movement of a stock supposes that...Ch. 5 - An image is partitioned into two regions, one...Ch. 5 - a. A fire station is to be located along a road of...Ch. 5 - The time (in hours) required to repair a machine...Ch. 5 - If U is uniformly distributed on (0,1), find the...Ch. 5 - Jones figures that the total number of thousands...Ch. 5 - Prob. 5.35PCh. 5 - The lung cancer hazard rate (t) of a t-year-old...Ch. 5 - Suppose that the life distribution of an item has...Ch. 5 - If X is uniformly distributed over (1,1), find (a)...Ch. 5 - Prob. 5.39PCh. 5 - If X is an exponential random variable with...Ch. 5 - If X is uniformly distributed over(a,b), find a...Ch. 5 - Prob. 5.42PCh. 5 - Find the distribution of R=Asin, where A is a...Ch. 5 - Let Y be a log normal random variable (see Example...Ch. 5 - The speed of a molecule in a uniform gas at...Ch. 5 - Show that E[Y]=0P{Yy}dy0P{Yy}dy Hint: Show that...Ch. 5 - Show that if X has density function f. then...Ch. 5 - Prob. 5.4TECh. 5 - Use the result that for a nonnegative random...Ch. 5 - Prob. 5.6TECh. 5 - The standard deviation of X. denoted SD(X), is...Ch. 5 - Let X be a random variable that takes on values...Ch. 5 - Show that Z is a standard normal random variable;...Ch. 5 - Let f(x) denote the probability density function...Ch. 5 - Let Z be a standard normal random variable Z and...Ch. 5 - Use the identity of Theoretical Exercises 5.5 .Ch. 5 - The median of a continuous random variable having...Ch. 5 - The mode of a continuous random variable having...Ch. 5 - If X is an exponential random variable with...Ch. 5 - Compute the hazard rate function of X when X is...Ch. 5 - If X has hazard rate function X(t), compute the...Ch. 5 - Prob. 5.18TECh. 5 - If X is an exponential random variable with mean...Ch. 5 - Prob. 5.20TECh. 5 - Prob. 5.21TECh. 5 - Compute the hazard rate function of a gamma random...Ch. 5 - Compute the hazard rate function of a Weibull...Ch. 5 - Prob. 5.24TECh. 5 - Let Y=(Xv) Show that if X is a Weibull random...Ch. 5 - Let F be a continuous distribution function. If U...Ch. 5 - If X is uniformly distributed over (a,b), what...Ch. 5 - Consider the beta distribution with parameters...Ch. 5 - Prob. 5.29TECh. 5 - Prob. 5.30TECh. 5 - Prob. 5.31TECh. 5 - Let X and Y be independent random variables that...Ch. 5 - Prob. 5.33TECh. 5 - The number of minutes of playing time of a certain...Ch. 5 - For some constant c. the random variable X has the...Ch. 5 - Prob. 5.3STPECh. 5 - Prob. 5.4STPECh. 5 - The random variable X is said to be a discrete...Ch. 5 - Prob. 5.6STPECh. 5 - To be a winner in a certain game, you must be...Ch. 5 - A randomly chosen IQ test taker obtains a score...Ch. 5 - Suppose that the travel time from your home to...Ch. 5 - The life of a certain type of automobile tire is...Ch. 5 - The annual rainfall in Cleveland, Ohio, is...Ch. 5 - Prob. 5.12STPECh. 5 - Prob. 5.13STPECh. 5 - Prob. 5.14STPECh. 5 - The number of years that a washing machine...Ch. 5 - Prob. 5.16STPECh. 5 - Prob. 5.17STPECh. 5 - There are two types of batteries in a bin. When in...Ch. 5 - Prob. 5.19STPECh. 5 - For any real number y define byy+=y,ify00,ify0 Let...Ch. 5 - With (x) being the probability that a normal...Ch. 5 - Prob. 5.22STPECh. 5 - Letf(x)={13ex1313e(x1)ifx0if0x1ifx1 a. Show that f...Ch. 5 - Prob. 5.24STPE
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.Similar questions
- The table below shows the number of chickens slaughtered during each month of 2021, as wel as the number of birds that was forecasted to be slaughtered each month using a 3-month moving average. The weights used to make these forecasts are w = 0.5, Wt 1 = 0.3, and w2 = 0.2. If you use a 3-month moving average with the same weights, how many birds would you forecast would be slaughtered is January 2022 (i e. one month after the last entry in the table). Slaughter Birds Slaughtered Forecast (Y.) 01/28/2021 6,045,000 6,335,011 02/28/2021 5,893.000 03/28/2021 6.686,000 6,084,900 04/28/2021 6,643,000 05/28/2021 0,648,000 6,322,348 06/28/2021 7,519,000 07/28/2021 6,980.000 08/28/2021 6,859,000 09/28/2021 6,722,000 7,213,977 10/28/2021 6,340,000 7,030,539 11/28/2021 5,768.000 12/28/2021 6,288.000 O a. 7,753,211 Date () ,WMA 6,249, 105 6,275,674 6,549,849 6,824,016 6,965 087 7,085,925 6.610,554 O b.6,335,011 O.6,368,054 Od.5,050,520arrow_forward2. This question is about logistic regression. The outcome variable is success (1=success, 0=failure), and we have two groups of observations: group A and group B. a. Assume that on average, the odds of success is x for group A members. What is the average probability of success (p) for group A? Please write down p as a function of x. Given an x, is there a unique p? b. Assume that on average, the odds ratio for success of group A over group B is 2. The average probability of success for group A is pA and that the average probability of success for group B is pg. Is the set of Paand pg unique? c. The logistic regression of success ~ group (link=logit) returns a coefficient estimate of -1.3863 for the dummy variable group (1=group A, 0=group B). Interpret this coefficient estimate.arrow_forwardAn engineer designs a circuit, seen below. In this system, if the first component fails, the functionality moves immediately to the second component and so on. The system only fails when the fifth component fails. Each component has a lifetime that is exponentially distributed with λ = 0.01 and components fail independently of one another. Define A, to be the length of time component i lasts. Let Y = the time at which the new system fails. Given 2 لنا 5 A-Exponential (0.01) Y=A1+A2+A3+A4+A5 1. Find the probability that this new system will last fewer than 50 hours.arrow_forward
- Please see the attached image, and answer the GREEN POLL MULTIPLE CHOICE questions!!!arrow_forwardCan gender, educational level, and age predict the odds that someone votes for a particular candidate in the election? Over 1500 voters were selected, and data were col-lected on the highest year of school completed, their age, and their gender. We wish to t a logistic regression model: log(1 p p ) = 0 + 1Age + 2Education + 3Gender, where p is the binomial probability that a person voted for candidate Johnson, and gender is coded as the indicator for female. The R output is given below. parameter df estimate s.e z p-value (Intercept) 1 .1119 .3481 .321 .748 Age 1 .0020 .0032 .613 .54 Education 1 -.0100 .0184 .547 .585 Gender 1 .4282 .1040 4.117 .000 Null deviance: 255.95 on 1499 degrees of freedom Residual deviance: 220.80 on 1496 degrees of freedom Write down the tted logistic regression and give a short summary about the data analysis . Calculate the probability of voting for Johnson for a…arrow_forwardThe population (in millions) and the violent crime rate (per 1000) were recorded for 10 metropolitan areas. The data are shown in the following table. Do these data provide evidence to reject the null hypothesis that p = 0 in favor of p + 0 at a = .05? (Give your answers correct to three decimal places.) Population 9.2 2.6 1.3 6.6 0.4 0.2 2.3 4.3 3.3 0.2 Crime Rate 11.9 9.1 7 8.7 8.1 8.1 9.5 8.5 6.7 (a) Calculate r. 79 (ii) Calculate the critical region. X (smaller value) X (larger value) -2.262 2.262 (b) State the appropriate conclusion. O Reject the null hypothesis, there is not significant evidence that p # 0. O Reject the null hypothesis, there Is significant evidence that p # 0. O Fail to reject the null hypothesis, there is not significant evidence that p + 0. O Fail to reject the null hypothesis, there is significant evidence that p # 0.arrow_forward
- “Normal” BMI is up to 25 kg/m2. A laboratory study is being conducted to determine energy expenditure for those who are overweight and/or obese. The researchers have enrolled only subjects with BMI above 25.0 and have quantified obesity as “units above normal”. For example, a subject with BMI of 32.3 is recorded as 7.3 (i.e. 32.3 – 25.0 = 7.3). Using this scheme, the mean obesity was found to be 8.7 kg/m2and the standard deviation was 6.4 kg/m2. If we convert the obesity measure used in this study back into conventional BMI (i.e., add 25.0 units to each measurement), what will the standard deviation be? Group of answer choices The standard deviation will be larger on the BMI scale because 25.0 units will be added back. The standard deviation will be the same 6.4 kg/m2 There is not enough information to determine this The standard deviation will be smaller on the BMI scale because, as a percentage of the whole scale, the difference between each subject and the mean will be…arrow_forwardWhich of the following is NOT an assumption made about the random error e in a simple linear regression model? A. The distribution of e is normal. B. The mean of e is Bo + B1x. C. The standard deviation of e is constant for all x values. D. €1, €2, ..., En are independent of one another.arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Continuous Probability Distributions - Basic Introduction; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=QxqxdQ_g2uw;License: Standard YouTube License, CC-BY
Probability Density Function (p.d.f.) Finding k (Part 1) | ExamSolutions; Author: ExamSolutions;https://www.youtube.com/watch?v=RsuS2ehsTDM;License: Standard YouTube License, CC-BY
Find the value of k so that the Function is a Probability Density Function; Author: The Math Sorcerer;https://www.youtube.com/watch?v=QqoCZWrVnbA;License: Standard Youtube License