For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains below a critical value yo (a deficit), preceded by and followed by periods in which the supplyexceeds this critical value (a surplus). An article proposes a geometric distribution with p = 0.365 for this random variable. (Round your answers to three decimal places.)(a) What is the probability that a drought lasts exactly 3 intervals? At most 3 intervals?exactly 3 intervalsat most 3 intervals(b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?

Given:1.a) The probability that a drought lasts exactly 3 intervals is obtained as below:Thus, the…

Answered: For a certain river, suppose the…

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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For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains below a critical value yo (a deficit), preceded by and followed by periods in which the supply exceeds this critical value (a surplus). An article proposes a geometric distribution with p = 0.388 for this random variable. (Round your answers to three decimal places.) (a) What is the probability that a drought lasts exactly 3 intervals? At most 3 intervals? exactly 3 intervals at most 3 intervals (b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?
Person P is walking with his dog every day. He decides to model the time intervals between dog encounters (i.e., how long does it take between two encounters) with the independent random variables Y1, . . ., Yn. Number of dogs encounters per day, the number of customers entering a store per hour, the number of bacteria per liter of water, etc. are classically modelled using the Poisson distribution. With an exponential distribution, on the other hand, is used for modelling intervals of between events and how long a light bulb lasts, for example. After learning this, person P decides to model the observations in such a way that the corresponding random variables Y1,..., Yn for a random sample, that is, independent observation, of the exponential distribution Exp(1/µ), µ > 0. The parameter μ > 0 is used as the statistical model parameter 1 which is the expected value of each observation random variable Yi. Derive (a) the joint density function f(y;µ) specifying the model. (b) the…
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For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains below a critical value y, (a deficit), preceded by and followed by periods in which the supply exceeds this critical value (a surplus). An article proposes a geometric distribution with p 0.364 for this random variable. (Round your answers to three decimal places.) (a) What is the probability that a drought lasts exactly 3 intervals? At most 3 intervals? exactly 3 intervals at most 3 intervals (b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?
3. Football goal scoring events arrive as a Poisson process in a a 90-minute match at a mean rate of 2.7 goals per match. Find the probability that an interval time is less than 30 minutes: (A) 0.0672 (B) 0.4066 (C) 0.5934 (D) 0.9328
A university is considering setting up an information desk manned by one employee. Based on information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 18 per hour. It takes an average of 2 minutes to answer a question. It is assumed that arrivals are Poisson and answer times are exponentially distributed. What is the arrival rate? (Include the units.) What is the service rate? (Include the units.) Find the probability that the employee is idle.
Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…

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