Chapters: Normal and Exponential random variables.Q: There exist naturally occurring random variables thatare neither discrete nor continuous. Suppose a group ofpeople is waiting for one more person to arrive beforestarting a meeting. Suppose that the arrival time of theperson is exponential with mean 4 minutes, and thatthe meeting will start either when the person arrives orafter 5 minutes, whichever comes first. Let X denotethe length of time the group waits before starting themeeting.- a. Find P(0

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Answered: :There exist naturally occurring random…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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= Suppose that independent Bernoulli trials, each having probability p 0.4, of being a success are performed until a total of r = 3 success is achieved. Let X be the number of trials required. a) What are the possible values for X? b) IfX = n, find P (X = n). c) What is the probability of having 3 success before having 5 failures?
4. Let X1, X2, ., Xn,... be a sequence of i.i.d. random variables with Poisson(A = 8) distribution. Prove that for some n, P(X1 + X2 +.+ Xn > 9n) < 0.001
Cards are picked sequentially without replacement from a well-shuffled deck of 52 cards until either all SPADES are found or all CLUBS are found. Let X denote the number of cards picked. Find E(X) using indicator random variables.
A second-stage smog alert has been called in a certain area of Los Angeles County in which there are 90 industrial firms. An inspector will visit 30 randomly selected firms to check for violations of regulations. (a) If 36 of the firms are actually violating at least one regulation, what is th nmf of the number of firms visited by the inspector that are in violation of at least one regulation? O Пx; 30, 0.4) O nb(x; 30, 0.4) O h(x; 30, 36, 90) О Бх;B 30, 0.4) O nb(x; 30, 36, 90) О Бх; 30, 36, 90) (b) If there are 900 firms in the area, of which 360 are in violation, approximate the pmf of part (a) by a simpler pmf. О hix; 30, 360, 900) O nb(x; 30, 0.4) O b(x; 30, 0.4) O nb(x; 30, 360, 900) O h(x; 30, 0.4) О Бix; 30, 360, 900) (c) For X = the number that are in violation among the 30 visited out of 900 firms, compute E(X) and V(X) both for the exact pmf and the approximating pmf in part (b). (Round your answers to two decimal places.) Compute E(X) and V(X) for the exact pmf. E(X) V(X)…
A and B agree to meet at a certain place between 1 PM and 2 PM. Suppose they arrive at the meeting place independently and randomly during the hour. Find the distribution of the length of time that A waits for B. (If B arrives before A, define A's waiting time as 0.)
4.a) Given a fair die, let X be the random variable denoting the result when the die is rolled. Find (i) E(X), (ii) E(X²), and (iii) V(X). b) Roll a fair die 30 times; the outcomes of these rolls are assumed to be independent. Use the central limit theorem to approximate the probability that a total > 110 is obtained. Use common sense to figure out how to do continuity correction (not using continuity correction will lose points).
2. A number U is selected at random between 0 and 1. Let the events A and B be "U differs from 1/2 by more than 1/4" and "1-U is less than 1/2", respectively. Find the events An B, Ān B, AU B.
6. Help plz
Suppose that you enter a fantasy baseball league. Suppose that the 2021 team budget, say , is randomly drawn from a uniform distribution on the interval , where the unit is U.S. million dollars. In addition, suppose that after the value has been observed , the 2022 team budget, say , is randomly drawn from a uniform distribution on the interval . In other words, the 2022 budget is at most as large as the 2021 budget. a) For any given value of x(50<x<350), obtain E[Y|X=x] b) In view of part (a), obtain E[Y|X] c) Atlanta Braves won the 2021 World Series title. Their estimated 2022 payroll is about $130 million. Would your 2022 fantasy baseball budget be on average larger than their 2022 payroll? Explain briefly.
Suppose X is a uniform random variable where X is from 0 to 10. What type of random variable is X? continuous and uncountably infinite discrete and finite continuous and finite discrete and uncountably infinite

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