Probability and Statistical Inference (9th Edition)
9th Edition
ISBN: 9780321923271
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 3.3, Problem 6E
If the moment-generating
(a) The
(b) The variance of X.
(c)
(d)
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Could you explain how the inequalities u in (0,1), we have 0 ≤ X ≤u-Y for any 0 ≤Y<u and u in (1,2), we either have 0 ≤ X ≤u-Y for any u - 1 < Y<1, or 0≤x≤1 for any 0 ≤Y≤u - 1 are obtained please. They're in the solutions but don't understand how they were derived.
Can you please explain how to find the bounds of the integrals for X and Y and also explain how to find the inequalites that satisfy X and Y. I've looked at the solutions but its not clear to me on how the inequalities and bounds of the integral were obtained. If possible could you explain how to find the bounds of the integrals by sketching a graph with the region of integration. Thanks
QUESTION 18 - 1 POINT
Jessie is playing a dice game and bets $9 on her first roll. If a 10, 7, or 4 is rolled, she wins $9. This happens with a probability of . If an 8 or 2 is rolled, she loses her $9. This has a probability of J. If any other number is rolled, she does not win or lose, and the game continues. Find the expected value for Jessie on her first roll.
Round to the nearest cent if necessary. Do not round until the final calculation.
Provide your answer below:
Chapter 3 Solutions
Probability and Statistical Inference (9th Edition)
Ch. 3.1 - Show that the mean, variance, and mgf of the...Ch. 3.1 - Let X be a continuous random variable with pdf...Ch. 3.1 - Customers arrive randomly at a bank tellers...Ch. 3.1 - If the mgf of X is M(t)=e5te4tt,t0andM(0)=1,, find...Ch. 3.1 - Let Y have a uniform distribution U(0,1), and let...Ch. 3.1 - A grocery store can order n watermelons from a...Ch. 3.1 - For each of the following functions, (i) find the...Ch. 3.1 - For each of the following functions, (i) find the...Ch. 3.1 - Prob. 9ECh. 3.1 - The pdf of X is f(x)=cx2,1x. (a) Calculate the...
Ch. 3.1 - The pdf of Y is g(y)=cy3,1y. (a) Calculate the...Ch. 3.1 - Sketch the graphs of the following pdfs and find...Ch. 3.1 - The logistic distribution is associated with the...Ch. 3.1 - Find the variances of each of the distributions...Ch. 3.1 - The life X (in years) of a voltage regulator of a...Ch. 3.1 - Let f(x)=(x+1)2,1x1. Find (a) 0.64, (b) q1=0.25,...Ch. 3.1 - An insurance agent receives a bonus if the loss...Ch. 3.1 - Prob. 18ECh. 3.1 - The total amount of medical claims (in $100000) of...Ch. 3.1 - Nicol (see References) lets the pdf of X be...Ch. 3.1 - Let X1,X2,...,Xk be random variables of the...Ch. 3.2 - Prob. 1ECh. 3.2 - Telephone calls arrive at a doctors office...Ch. 3.2 - Let X have an exponential distribution with mean...Ch. 3.2 - Let F(x) be the cdf of the continuous-type random...Ch. 3.2 - There are times when a shifted exponential model...Ch. 3.2 - A certain type of aluminum screen 2 feet in width...Ch. 3.2 - Find the moment-generating function for the gamma...Ch. 3.2 - If X has a gamma distribution with =4 and =2, find...Ch. 3.2 - If the moment-generating function of a random...Ch. 3.2 - Use the moment-generating function of a gamma...Ch. 3.2 - Let X have a gamma distribution with parameters ...Ch. 3.2 - Let X equal the number of alpha particle emissions...Ch. 3.2 - If X is x2(23), find the following: (a)...Ch. 3.2 - If X is x2(12), find constants a and b such that...Ch. 3.2 - Prob. 15ECh. 3.2 - Cars arrive at a tollbooth at a mean rate of five...Ch. 3.2 - If 15 observations are taken independently from a...Ch. 3.2 - Say the serum cholesterol level (X) of U.S. males...Ch. 3.2 - A bakery sells rolls in units of a dozen. The...Ch. 3.2 - The initial value of an appliance is $700 and its...Ch. 3.2 - A loss (in $100000) due to fire in a building has...Ch. 3.2 - Prob. 22ECh. 3.2 - Prob. 23ECh. 3.2 - Prob. 24ECh. 3.3 - If Z is N(0,1), find (a) P(0.47Z2.13). (b)...Ch. 3.3 - If Z is N(0,1), find (a) P(0Z0.78). (b) P(2.46Z0)....Ch. 3.3 - If Z is N(0,1), find values of c such that (a)...Ch. 3.3 - Find the values of (a) z0.10, (b) z0.05, (c)...Ch. 3.3 - If X is normally distributed with a mean of 6 and...Ch. 3.3 - If the moment-generating function of X is...Ch. 3.3 - If X is N(650,400), find (a) P(600X660). (b) A...Ch. 3.3 - Prob. 8ECh. 3.3 - Find the distribution of W=X2 when (a) X is...Ch. 3.3 - If X is N(,2) show that Y=aX+b is N(a,+b,a22),a0,...Ch. 3.3 - A candy maker produces mints that have a label...Ch. 3.3 - Prob. 12ECh. 3.3 - The serum zinc level X in micrograms per deciliter...Ch. 3.3 - The strength X of a certain material is such that...Ch. 3.3 - The fill problem is important in many industries,...Ch. 3.3 - The graphs of the moment-generating functions of...Ch. 3.3 - Prob. 17ECh. 3.4 - Let the life W (in years) of the usual family car...Ch. 3.4 - Suppose that the length W of a mans life does...Ch. 3.4 - Let Y1 be the smallest observation of three...Ch. 3.4 - Prob. 4ECh. 3.4 - Let X be a random variable of the mixed type...Ch. 3.4 - Let X be a random variable of the mixed type...Ch. 3.4 - Prob. 7ECh. 3.4 - Find the mean and variance of X if the cdf of X is...Ch. 3.4 - Consider the following game: A fair die is rolled....Ch. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Let X have an exponential distribution with =1;...Ch. 3.4 - A loss X on a car has a mixed distribution with...Ch. 3.4 - A customer buys a $1000 deductible policy on her...Ch. 3.4 - A certain machine has a life X that has an...Ch. 3.4 - Prob. 16ECh. 3.4 - Some banks now compound daily, but report only on...Ch. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 3.4 - Let X be the failure time (in months) of a certain...Ch. 3.4 - In a medical experiment, a rat has been exposed to...
Additional Math Textbook Solutions
Find more solutions based on key concepts
23. A plant nursery sells two sizes of oak trees to landscapers. Large trees cost the nursery $120 from the gro...
College Algebra (Collegiate Math)
1. How is a sample related to a population?
Elementary Statistics: Picturing the World (7th Edition)
For Problems 23-28, write in simpler form, as in Example 4. logbFG
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Provide an example of a qualitative variable and an example of a quantitative variable.
Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561
In Exercises 5-36, express all probabilities as fractions.
23. Combination Lock The typical combination lock us...
Elementary Statistics
Check Your Understanding
Reading Check Complete each sentence using > or < for □.
RC1. 3 dm □ 3 dam
Basic College Mathematics
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
- 5 of 5 (i) Let a discrete sample space be given by Ω = {ω1, 2, 3, 4}, Total marks 12 and let a probability measure P on be given by P(w1) 0.2, P(w2) = 0.2, P(w3) = 0.5, P(w4) = 0.1. = Consider the random variables X1, X2 → R defined by X₁(w3) = 1, X₁(4) = 1, X₁(w₁) = 1, X₁(w2) = 2, X2(w1) = 2, X2(w2) = 2, X2(W3) = 1, X2(w4) = 2. Find the joint distribution of X1, X2. (ii) [4 Marks] Let Y, Z be random variables on a probability space (N, F, P). Let the random vector (Y, Z) take on values in the set [0,1] × [0,2] and let the joint distribution of Y, Z on [0,1] × [0,2] be given by 1 dPy,z(y, z) (y²z + y²²) dy dz. Find the distribution Py of the random variable Y. [8 Marks]arrow_forwardTotal marks 16 5. Let (,,P) be a probability space and let X : → R be a random variable whose probability density function is given by f(x) = }}|x|e¯|×| for x Є R. (i) (ii) Find the characteristic function of the random variable X. [8 Marks] Using the result of (i), calculate the first two moments of the random variable X, i.e., E(X") for n = 1, 2. (iii) What is the variance of X? [6 Marks] [2 Marks]arrow_forwardTotal marks 16 5. Let (N,F,P) be a probability space and let X : N → R be a random variable such that the probability density function is given by f(x)=ex for x € R. (i) Find the characteristic function of the random variable X. [8 Marks] (ii) Using the result of (i), calculate the first two moments of the random variable X, i.e., E(X") for n = 1,2. (iii) What is the variance of X. [6 Marks] [2 Marks]arrow_forward
- 6. Let P be the standard normal distribution, i.e., P is the proba- bility measure on (R, B(R)) given by 1 dP(x) = 를 = e dx. √2πT Consider the random variables 21 fn(x) = (1 + x²) en+2, x Є R, n Є N. Using the dominated convergence theorem, prove that the limit Total marks 9 exists and find it. lim E(fn) n∞ [9 Marks]arrow_forward6. Let X be a random variable taking values in (0,∞) with proba- bility density function fx(u) = 5e5u u > 0. Total marks 8 Let Y = X2. Find the probability density function of Y. [8 Marks]arrow_forward5. Let a probability measure P on ([0,3], B([0,3])) be given by 1 dP(s): = ½ s² ds. 9 Consider a random variable X : [0,3] → R given by X(s) = s², sc [0,3]. S Total marks 7 Find the distribution of X. [7 Marks]arrow_forward
- Problem: The probability density function of a random variable is given by the exponential distribution Find the probability that f(x) = {0.55e−0.55x 0 < x, O elsewhere} a. the time to observe a particle is more than 200 microseconds. b. the time to observe a particle is less than 10 microseconds.arrow_forwardProblem: The probability density function of a random variable is given by the exponential distribution Find the probability that f(x) = {0.55e-0.55 x 0 < x, O elsewhere} a. the time to observe a particle is more than 200 microseconds. b. the time to observe a particle is less than 10 microseconds.arrow_forwardUnknown to a medical researcher, 7 out of 24 patients have a heart problem that will result in death if they receive the test drug. 5 patients are randomly selected to receive the drug and the rest receive a placebo. What is the probability that less than 4 patients will die? Express as a fraction or a decimal number rounded to four decimal places.arrow_forward
- Was wanting to check if my calculations were correct Suppose 52% of the population has a college degree. If a random sample of size 808 is selected, what is the probability that the proportion of persons with a college degree will be less than 54%? Round to four decimal places. after following the formula I got 0.8724arrow_forwardAt the beginning of each semester, students at the University of Minnesota receive one prepaid copy card that allows them to print from the copiers and printers on campus. The amount of money remaining on the card can be modeled by a linear equation where A represents how much remains on the card (in dollars) and p represents the number of pages that the student has printed. The graph of this linear equation is given below. 100 90 80 70 60 50 40 30 20 10 0 A = Amount on Card ($) 0 200 400 600 800 1000 1200 1400 1600 p = Number of Pages Printed What information does the vertical intercept tell you (represent) for this problem? Be sure to include specific details in your answer -- your answer should have both quantitative and qualitative data to describe the answer in terms of the question.arrow_forwardData management no 2 thanksarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
Statistics 4.1 Point Estimators; Author: Dr. Jack L. Jackson II;https://www.youtube.com/watch?v=2MrI0J8XCEE;License: Standard YouTube License, CC-BY
Statistics 101: Point Estimators; Author: Brandon Foltz;https://www.youtube.com/watch?v=4v41z3HwLaM;License: Standard YouTube License, CC-BY
Central limit theorem; Author: 365 Data Science;https://www.youtube.com/watch?v=b5xQmk9veZ4;License: Standard YouTube License, CC-BY
Point Estimate Definition & Example; Author: Prof. Essa;https://www.youtube.com/watch?v=OTVwtvQmSn0;License: Standard Youtube License
Point Estimation; Author: Vamsidhar Ambatipudi;https://www.youtube.com/watch?v=flqhlM2bZWc;License: Standard Youtube License