A First Course In Probability, Global Edition
10th Edition
ISBN: 9781292269207
Author: Ross, Sheldon
Publisher: PEARSON
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Chapter 10, Problem 10.4P
Present a method for simulating a random variable having distribution
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Problem: The probability density function of a random variable is given by the exponential
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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.
Unknown 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.
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 0.8724
Chapter 10 Solutions
A First Course In Probability, Global 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
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- 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
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