Let X1 and X2 be independent with normal distributions N (6, 1) and N (7, 1), respectively. Find P(X1 >X2). Hint: Write P(X1 > X2) = P(X1 - X2 > 0) and determine the distribution of X1 - X2.

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Answered: X2). Hint: Write P(X1 > X2) = P(X1-X2 >…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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What is the income distribution of super shoppers? A supermarket super shopper is defined as a shopper for whom at least 70% of the items purchased were on sale or purchased with a coupon. In the following table, income units are in thousands of dollars, and each interval goes up to but does not include the given high value. The midpoints are given to the nearest thousand dollars. (a) Using the income midpoints x and the percent of super shoppers, do we have a valid probability distribution? Explain. a) Yes. The events are indistinct and the probabilities sum to less than 1. b) Yes. The events are distinct and the probabilities sum to 1. c) Yes. The events are distinct and the probabilities do not sum to 1. d) No. The events are indistinct and the probabilities sum to 1. e) No. The events are indistinct and the probabilities sum to more than 1. (b) Use a histogram to graph the probability distribution of part (a). (c) Compute the expected income μ of a super shopper. (Round…
The binomial distribution is used when there are exactly two mutually exclusive outcomes of a trial. These outcomes are appropriately labeled "success" and " failure". The binomial distribution is used to obtain the probability of observing x success in N trials, with the probability of success on a single trial denoted by p. The binomial distribution assumes that p is fixed for all trial. Let p = 1/2 and q = 1/2. If a coin is tossed 7 times, what is the probability that we will obtain a success of up to 4 heads?
The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20-39 who regularly skip eating breakfast is 0.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size n = 500 of young adults ages 20–39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, X, in Lance's sample who regularly skip breakfast is greater than 126. You may find table of critical values helpful. Express the result as a decimal precise to three places. P(X > 126) :
O Suppose that you enter a fantasy basketball league. Suppose that the 2022 team budget, say X, is randomly drawn from a uniform distribution on the interval [90, 210], where the unit is U.S. million dollars. In addition, suppose that after the value X = x has been observed (90 < x < 210), the 2023 team budget, say Y, is randomly drawn from a uniform distribution on the interval [x, 210]. In other words, the 2023 budget is at least as large as the 2022 budget. (a) For any given value of x (90 < x < 210), obtain E[Y|X = x]. (b) In view of part (i), obtain E[Y|X]. (c) What is the difference between E[Y|X = x] and E[Y|X]?
Calculate the probability that is between 0.2 and 0.7, if x is uifomly distributed in the interval [0,1]
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Which of the following are specified by the central limit theorem? a. the mean of a specific sample from the distribution of sample means b. the mean of the distribution of sample means c. the shape of the distribution of sample means d. the variability for the distribution of sample means
r.s. ork. Let X₁, X₂, X3, X4 ~ N (0,8) & X5 ~ N(1,4) w/ is independent from X₁, X₂, X3 & X4, Find the distribution of each of the following 2 4(x₂-1)² X₁²³+ X₂² O X4-X3 8 2 2 @ X ² + x ² + x ² + x +² (2) 8 (3) √₂ (X4~X3) √√x₁²³²+x² + x³ + x²³² 2 4 2 3 © 2X₁² + 2X₂² X₁² + X² ² + X ² + X ² 2
In a Binomial Distribution, if p = q, then P(X = x) is given by? A) „G (0.5)" B) „G (0.5)" C) „G pln-x) D) „C, plax) B. C
Suppose that you enter a fantasy basketball league. Suppose that the 2022 team budget, say X, is randomly drawn from a uniform distribution on the interval [90, 210], where the unit is U.S. million dollars. In addition, suppose that after the value X = x has been observed (90 < x < 210), the 2023 team budget, say Y, is randomly drawn from a uniform distribution on the interval [x, 210]. In other words, the 2023 budget is at least as large as the 2022 budget. (a) For any given value of x (90 < x < 210), obtain E[Y|X = x]. (b) In view of part (i), obtain E[Y|X]. (c) What is the difference between E[Y|X = x] and E[Y|X]? (d) Obtain E[Y]. That is, what is the expected value of your 2023 fantasy basketball budget? (e) Golden State Warriors won the 2022 NBA finals. Their estimated 2022 payroll is about $194 million. Would your 2023 fantasy basketball budget be on average larger than Golden State Warriors' 2022 payroll? Explain briefly.

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X2). Hint: Write P(X1 > X2) = P(X1-X2 > 0) and determine the distribution of X1 - X2. !!