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
Videos
Textbook Question
Chapter 5.4, Problem 11E
Let X and Y equal the outcomes when two fair six-sided dice are rolled. Let
Assuming independence, find the pmf of W when
(a) The first die has three faces numbered 0 and three faces numbered 2, and the second die has its faces numbered 0,1, 4, 5, 8, and 9.
(b) The faces on the first die are numbered 0,1,2,3,4, and 5, and the faces on the second die are numbered 0, 6, 12, 18, 24, and 30.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Consider rolling 2 3-sided dice. Let X = the sum of the dice. Let Y = the product of the dice.
a Find the COV(X,Y)
b. If a casino will pay the double the sum of the dice plus the product of the dice, would you play if they charged $6 to play?
A pair of tetrahedral dice are rolled (see Exercise 30.8). Let X be the sum of the two
numbers and let y be the product.
Find E(X) and E(Y).
You play a game in which you roll a die and you win (in dollars) the square of the
number on the die. For example, if you roll a 5, then you win $25. On average, how
much money would you expect to receive per play of this game?
Solve this question:
4. One urn contains one blue ball (labeled B1) and three red balls (labeled R1, R2, and R3). A second urn contains two red balls (R4 and R5) and two blue balls (B2 and B3). An experiment is performed in which one of the two
urns is chosen at random and then two balls are randomly chosen from it, one after the other without replacement.
a. Construct the possibility tree showing all possible outcomes of this experiment
. b. What is the total number of outcomes of this experiment ?c. What is the probability that two red balls are chosen?
USe pencil and paper to solve this question. showw your work as well. Dont use AI
Chapter 5 Solutions
Probability and Statistical Inference (9th Edition)
Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Let X have a gamma distribution with =3 and =2....Ch. 5.1 - The pdf of X is f(x)=2x,0x1. (a) Find the cdf of...Ch. 5.1 - Prob. 5ECh. 5.1 - Let X have a logistic distribution with pdf...Ch. 5.1 - A sum of $50000 is invested at a rate R, selected...Ch. 5.1 - The lifetime (in years) of a manufactured product...Ch. 5.1 - Statisticians frequently use the extreme extreme...Ch. 5.1 - Prob. 10E
Ch. 5.1 - Let X have a Cauchy distribution. Find (a) P(X1)....Ch. 5.1 - Let f(x)=1[(1+x2)],x, be the pdf of the Cauchy...Ch. 5.1 - If X is N(,2), then M(t)=E(etX)=exp(t+2t22),t. We...Ch. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.2 - Let X1,X2, denote two independent random...Ch. 5.2 - Let X1 and X2 be independent chi-square random...Ch. 5.2 - Prob. 3ECh. 5.2 - Let the distribution of W be F(9, 24). Find the...Ch. 5.2 - Let the distribution of W be F(8. 4). Find the...Ch. 5.2 - Let X1 and X2 have independent gamma distributions...Ch. 5.2 - Let X1 and X2 be independent chi-square random...Ch. 5.2 - Let X have a beta distribution with parameters ...Ch. 5.2 - Determine the constant c such that...Ch. 5.2 - When and are integers and0p1, we have...Ch. 5.2 - Evaluate 00.4(7)(4)(3)y3(1y)2dy (a) Using...Ch. 5.2 - Let W1,W2 be independent, each with a Cauchy...Ch. 5.2 - Let X1, X2 be independent random variables...Ch. 5.2 - Prob. 14ECh. 5.2 - In Example 5.2-6, verify that the given...Ch. 5.2 - Let W have an F distribution with parameters r1...Ch. 5.3 - Let X1 and X2 be a random sample of size n=2 from...Ch. 5.3 - Let X1,X2,X3 be three independent random variables...Ch. 5.4 - Let X1+X2+X3 be a random sample of size 3 from the...Ch. 5.4 - Let X1 and X2 have independent distributions...Ch. 5.4 - Prob. 3ECh. 5.4 - Generalize Exercise 5.4-3 by showing that the sum...Ch. 5.4 - Let Z1,Z2,....,Z7 be a random sample from the...Ch. 5.4 - Let X1,X2,X3,X4,X5 be a random sample of size 5...Ch. 5.4 - Let X1,X2,X3 denote a random sample of size 3 from...Ch. 5.4 - Let W=X1+X2+...+Xh, a sum of h mutually...Ch. 5.4 - Let X and Y, with respective pmfs f(x) and g(y),...Ch. 5.4 - Let X equal the outcome when a fair four-sided die...Ch. 5.4 - Let X and Y equal the outcomes when two fair...Ch. 5.4 - Let X and Y be the outcomes when a pair of fair...Ch. 5.4 - Let X1,X2,...,X8 be a random sample from a...Ch. 5.4 - The number of accidents in a period of one week...Ch. 5.4 - Given a fair four-sided die, let Y equal the...Ch. 5.4 - The number X of sick days taken during a year by...Ch. 5.4 - In a study concerning a new treatment of a certain...Ch. 5.4 - The number of cracks on a highway averages 0.5 per...Ch. 5.4 - A doorman at a hotel is trying to get three taxic...Ch. 5.4 - The time X in minutes of a visit to a...Ch. 5.4 - Let X and Y be independent with distributions...Ch. 5.4 - Let X1 and X2 be two independent random variables....Ch. 5.4 - Let X be N(0,1). Use the mgf technique to show...Ch. 5.5 - Let X1,X2...,X16, be a random sample from a normal...Ch. 5.5 - Let X be N(50,36). Using the same set of axes,...Ch. 5.5 - Let X equal the widest diameter (in millimeters)...Ch. 5.5 - Let X equal the weight of the soap in a 6-pound...Ch. 5.5 - Let X equal the weight (in grams) of a nail of the...Ch. 5.5 - Let X1,X2,...,X100 be a random sample from N(,4),...Ch. 5.5 - Suppose that the distribution of the weight of a...Ch. 5.5 - Let X denote the wing length in millimeters of a...Ch. 5.5 - Suppose that the length of life in hours (say, X)...Ch. 5.5 - A consumer buys n light bulbs, each of which has a...Ch. 5.5 - A marketing research firm suggests to a comp any...Ch. 5.5 - Let the independent random variables X1 and X2 be...Ch. 5.5 - Prob. 13ECh. 5.5 - Let T have at distribution with r degrees of freed...Ch. 5.5 - Let the distribution of T be t(17). Find (a)...Ch. 5.5 - Prob. 16ECh. 5.6 - Let X be the mean of a random sample of size 12...Ch. 5.6 - Let Y=X1+X2+....+X15 be the sum of a random sample...Ch. 5.6 - Let X be the mean of a random sample of size 36...Ch. 5.6 - Approximate P(39.75X41.25), where X is the mean of...Ch. 5.6 - Let X1,X2,...,X18 be a random sample of size 18...Ch. 5.6 - A random sample of size ii = 18 is taken from the...Ch. 5.6 - Let X equal the maximal oxygen intake of a human...Ch. 5.6 - Let X equal the weight in grams of a miniature...Ch. 5.6 - In Example 5.6-4, with n=4, compute P(1.73.2) and...Ch. 5.6 - Prob. 10ECh. 5.6 - The tensile strength X of paper, in pounds per...Ch. 5.6 - At certain times during the year, a bus company...Ch. 5.6 - Prob. 13ECh. 5.6 - Suppose that the sick leave taken by the typical...Ch. 5.7 - Let the distribution of Y be b(25,1/2). Find the...Ch. 5.7 - Suppose that among gifted seventh-graders who...Ch. 5.7 - A public opinion poll in Southern California was...Ch. 5.7 - Let X equal the number out of n=48 mature aster...Ch. 5.7 - Let X1,X2,...,X48 be a random sample of size 48...Ch. 5.7 - In adults, the pneumococcus bacterium causes 70%...Ch. 5.7 - Let X equal the number of alpha particles emitted...Ch. 5.7 - A candy maker produces mints that have a label...Ch. 5.7 - Let X1,X2,...,X30 be a random sample of size 30...Ch. 5.7 - Prob. 10ECh. 5.7 - On January 1 of a given year, a college basketball...Ch. 5.7 - If X is b(100,0.1), find the approximate value of...Ch. 5.7 - Let X1,X2,...,X36 be a random sample of size 36...Ch. 5.7 - A die is rolled 24 independent times. Let V be the...Ch. 5.7 - In the United States, the probability that a child...Ch. 5.7 - Let X equal the sum of n=100 Bernoulli trials....Ch. 5.7 - The number of trees in one acre has a Poisson...Ch. 5.7 - Assume that the background noise X of a digital...Ch. 5.8 - If X is a random variable with mean 33 and...Ch. 5.8 - If E(X)=17 and E(X2)=298, use Chebyshevs...Ch. 5.8 - Let X denote the outcome when a fair die is...Ch. 5.8 - If Y is b(n,0.5), give a lower bound for...Ch. 5.8 - If the distribution of Y is b(n,0.25), give a...Ch. 5.8 - Let X be the mean of a random sample of size n=15...Ch. 5.8 - Suppose that W is a continuous random variable...Ch. 5.9 - Let Y be the number of defectives in a box of 50...Ch. 5.9 - The probability that a certain type of inoculation...Ch. 5.9 - Let S2 be the sample variance of a random sample...Ch. 5.9 - Let Y be x2(n). Use the central limit theorem to...Ch. 5.9 - Let Y have a Poisson distribution with mean 3n....
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
- An urn contains twelve chips—four red, three black, and five white. A sample of size 4 is to be drawn without replacement. Let X denote the number of white chips in the sample, Y the number of red. Find FX,Y (1, 2).arrow_forwardLet A = {1,2,3} and B = {2,7,9}· Then (AN B)UA = %3D None of the these OANB | B O Aarrow_forward2. Let U= { 11, 12, 13, 14, 15, 16, 17, 18, 19) and A = {12, 14, 16, 18} , B = {12, 15, 16, 19}, and C = {11, 13, 15, 17} %3D Find An B =arrow_forward
- 1. Which is the missing tile? A C E Farrow_forwardExercise ( H.W): 4/ A survey of 500 television watchers produced the following information. football games 195 = basketball games 115 = hockey games hockey and basketball 285watch 50 = 45 = football and basketball 70 football and hockey %3D 50 do not watch any of three games a/ How many people in the survey watch all three games b/ How many people in the survey watch exactly one of the three gamesarrow_forwardThe variable with the largest positive Pj – Zj value is the a. artificial variable b. entering variable c. slack variable d leaving variablearrow_forward
- Nonearrow_forwardTravis plays Grog, a barbarian, in Matt's Dungeons & Dragons campaign. Travis has a feature that allows Grog to critically hit when he rolls either a 19 or a 20 when rolling for an attack using a 20-sided die. Thus, Grog will critically hit about 10% of the time. A statistician randomly selects 20 attack rolls Travis makes from throughout the campaign. Let X count the number of critical hits Grog makes in the group of 20 of Travis' attack rolls randomly selected by the statistician. Select the appropriate distribution for the random variable X. Group of answer choices X∼Bin(20,0.1) X∼Poisson(20) X∼Poisson(0.1) X∼Bin(0.1,20) Compute the probability that Grog critically hits between 3 and 5 times (inclusive) in the 20 attack rolls selected by the statistician. Compute the mean number of critical hits by Grog in a randomly selected group of 20 attacks. Using the mean and standard deviation, complete the description below. "In a randomly selected group of 20…arrow_forwardThe head of the production department of FPDJ Electronic Company wants to determine the relationship between the number of workers who assemble a particular electronic gadget and the number of units of that product assembled per day. Totals: No. of Workers No. of Units Produced Y 120 180 220 224 176 320 270 275 1785 X 10 12 14 16 13 20 18 17 120 XY 1200 2160 3080 3584 2288 6400 4860 4675 28247 y² 100 14400 144 32400 196 48400 256 50176 169 30976 400 102400 324 72900 289 75625 1878 427277 X² Using the best-fit line (regression line), estimate the number of units that will be produced if there will be 19 workers.arrow_forward
- To medical textb.. Ibrary ocks % 1 5 X Playing a Game-Quizizz O CK12 G5 of 5] Persepolis: T.. 96RCECM8T 252B1YHXCIQjavshtFacfQvExaXL Medical Terminology 6 الالالالا Type your answer in the boxes Owen's house is 12 blocks from the library and 8 blocks from the school. The library is 9 blocks from the school. What is the approximate measure, to the nearest degree, of the angle between the path from Owen's house to the library and the path from Owen's house to the school? DELL y Desmos | Graphing Calculator X & 7 u Nocti practice 8 9 P IL O O 4529 5775 [] SUBMIT + 11 G backspa BBarrow_forwardA Ph.D. graduate has applied for a job with two colleges: A and B. The graduate feels that she has a 60% chance of receiving an offer from college A and a 50% chance of receiving an offer from college B. If she receives an offer from college B, she believes that she has an 80% chance of receiving an offer from college A. Let A = receiving an offer from college A, and let B = receiving an offer from college B. a. What is the probability that both colleges will make her an offer? b. What is the probability that at least one college will make her an offer? c. If she receives an offer from college B, what is the probability that she will not receive an offer from college A?arrow_forwardSuppose й 3D (-2, -3, -3), ѣ %3D (-5, -2, -3) and W %3 (0, 0, —5). Then: u • v= и • W= v• w= U• v= u . (ü + w)=arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,
Elementary Geometry for College Students
Geometry
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Introduction to experimental design and analysis of variance (ANOVA); Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=vSFo1MwLoxU;License: Standard YouTube License, CC-BY