A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 10, Problem 10.2P
To determine
To calculate: technique for simulating random variable using density
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
At 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.
Data management no 2 thanks
G12 Data Management please help on the first question no 1 below
Chapter 10 Solutions
A First Course in Probability (10th Edition)
Ch. 10 - The following algorithm will generate a random...Ch. 10 - Prob. 10.2PCh. 10 - Give a technique for simulating a random variable...Ch. 10 - Present a method for simulating a random variable...Ch. 10 - Use the inverse transformation method to present...Ch. 10 - Give a method for simulating a random variable...Ch. 10 - Let F be the distribution functionF(x)=xn0x1 a....Ch. 10 - Prob. 10.8PCh. 10 - Suppose we have a method for simulating random...Ch. 10 - Prob. 10.10P
Ch. 10 - Use the rejection method with g(x)=1,0x1, to...Ch. 10 - Prob. 10.12PCh. 10 - Prob. 10.13PCh. 10 - Prob. 10.14PCh. 10 - Prob. 10.15PCh. 10 - Let X be a random variable on (0, 1) whose density...Ch. 10 - Prob. 10.1STPECh. 10 - Prob. 10.2STPECh. 10 - Prob. 10.3STPECh. 10 - If X is a normal random variable with mean and...Ch. 10 - Prob. 10.5STPE
Knowledge Booster
Similar questions
- Total marks 14 4. Let X and Y be random variables on a probability space (N, F, P) that take values in [0, ∞). Assume that the joint density function of X and Y on [0, ∞) × [0, ∞) is given by f(x, y) = 2e-2x-y Find the probability P(0 ≤ X ≤ 1,0 ≤ y ≤ 2). (ii) spectively. [6 Marks] Find the the probability density function of X and Y, re- [5 Marks] 111) Are the X and Y independent? Justify your answer! [3 Marks]arrow_forwardTotal marks 17 4. Let (,,P) be a probability space and let X : → R be a ran- dom variable that has Gamma(2, 1) distribution, i.e., the distribution of the random variable X is the probability measure on ((0, ∞), B((0, ∞))) given by (i) dPx(x) = xex dx. Find the characteristic function of the random variable X. [8 Marks] (ii) Using the result of (i), calculate the first three moments of the random variable X, i.e., E(X") for n = 1, 2, 3. Using Markov's inequality involving E(X³), (iii) probability P(X > 10). [6 Marks] estimate the [3 Marks]arrow_forward1. There are 8 balls in an urn, of which 6 balls are red, 1 ball is blue and 1 ball is white. You draw a ball from the urn at random, note its colour, do not return the ball to the urn, and then draw a second ball, note its colour, do not return the ball to the urn, and finally draw a third ball, note its colour. (i) (Q, F, P). Describe the corresponding discrete probability space [7 Marks] (ii) Consider the following event, A: At least one of the first two balls is red.arrow_forward
- 3. Consider the following discrete probability space. Let = {aaa, bbb, ccc, abc, acb, bac, bca, cab, cba}, i.e., consists of 3-letter 'words' aaa, bbb, ccc, and all six possible 3-letter 'words' that have a single letter a, a single letter b, and a single letter c. The probability measure P is given by 1 P(w) = for each weΩ. 9 Consider the following events: A: the first letter of a 'word' is a, B: the second letter of a 'word' is a, C: the third letter of a 'word' is a. answer! Decide whether the statements bellow are true or false. Justify your (i) The events A, B, C are pairwise independent. (ii) The events A, B, C are independent. Total marks 7 [7 Marks]arrow_forwardLet X and Y have the following joint probability density function: fxy(x,y) =1/(x²²), for >>1, y>1 0, otherwise Let U = 5XY and V = 3 x. In all question parts below, give your answers to three decimal places (where appropriate). (a) The non-zero part of the joint probability density function of U and V is given by fu,v(u,v) = A√³uc for some constants A, B, C. Find the value of A. Answer: 5 Question 5 Answer saved Flag question Find the value of B. Answer: -1 Question 6 Answer saved P Flag question (b) The support of (U,V), namely the values of u and vthat correspond to the non-zero part of fu,v(u,v) given in part (a), is given by:arrow_forwardTotal marks 13. 3. There are three urns. Urn I contains 3 blue balls and 5 white balls; urn II contains 2 blue balls and 6 white balls; urn III contains 4 blue balls and 4 white balls. Rolling a dice, if 1 appears, we draw a ball from urn I; if 4 or 5 or 6 appears, we draw a ball from urn II; if 2, or 3 appears, we draw a ball from urn III. (i) What is the probability to draw a blue ball? [7 Marks] (ii) Assume that a blue ball is drawn. What is the probability that it came from Urn I? [6 Marks] Turn over. MA-252: Page 3 of 4arrow_forward
- 3. Consider the discrete probability space with the sample space = {a, b, c, d, e, f, g, h} and the probability measure P given by P(w) for each wEN. Consider the following events: A = {a, c, e, g}, B = {b, c, d, e}, C = = {a, b, d, g}. Decide whether the statements bellow are true or false. Justify your answer! (i) The events A, B, C are pairwise independent. (ii) The events A, B, C are independent. Total marks 6 [6 Marks]arrow_forward2. space Consider the discrete probability space (N, F, P) with the sample N = {W1 W2 W3 W4 W5, W6, W7, W8, W9, W10, W11, W12}, is the power of 2, and the probability measure P is given by 1 P(wi) for each i = 1, 12. 12 Consider the following events: A = {W1, W3, W5, W7, W9, W11}, C = B = {W1, WA, W7, W8, W9, W12}, = {W3, WA, W5, W6, W9, W12}. Decide whether the statements bellow are true or false. Justify your answer! (i) The events A, B, C are pairwise independent. [5 Marks] Total marks 8 (ii) The events A, B, C are independent. [3 Marks]arrow_forwardshould my answer be 2.632 or -2.632?arrow_forward
- 2. Alice has three unfair coins. The first coin shows heads with proba- bility 0.3 and tails with probability 0.7. The second coin shows heads with probability 0.9 and tails with probability 0.1. The third coin shows heads with probability 0.4 and tails with probability 0.6. First, Alice throws a dice. If the dice yields a 1 or 2, Alice tosses the first coin. If the dice yields a 3, Alice tosses the second coin. If the dice yields a 4 or 5, or 6, Alice tosses the third coin. (i) What is the probability of the following event: as a result of throwing the dice and then tossing a coin, tails appear. [7 Marks] Assume a coin shows tails. What is the probability that Alice (ii) tossed (a) the first coin; (b) the second coin; Total marks 11 (c) the third coin? [4 Marks]arrow_forwardIn a Poisson process with A = 500 arrivals per day, find the approximate probability that the thousandth arrival comes between 47.5 and 48.5 hours after the start of observations.arrow_forwardSuppose you generate 300 independent observations X1, ..., X300 from a Uniform(0,3) distribution. a) What is the approximate distribution of X? b) What is the approximate probability that X is less than 1.57? c) What is the approximate probability that the sum S300 = X₁++X300 is between 442 and 483?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning