We model the random amount of time (in hours) it takes to receive tech support with theprobability density functionf(t)=e, t> 0.We are uncertain about the rate parameter A (which gives the average number of customersserved per hour), and give it a Gamma prior distribution with parameters a = 8 and ẞ = 0.5.A random sample of 4 customers yields service times of:t₁ = 0.3, t2 = 0.1, t3 = 0.5, t4 = 0.3. Compute the posterior distribution for A.

We need to find the posterior distribution of the rate parameter λ given the service times observed…

Answered: We model the random amount of time (in…

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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A large insurance company indicates that 78% of the policy holders have at least one health issues and 22% do not health issues. Let Y1 be a random variable defined as Y1 = 0, if the policy holder does not have any health issues; Y1 = 1, if the if the policy holder have health issues. Write the probability distribution of Y1, E(Y1) and Var(Y1).
If the random variable x has a Poisson Distribution with mean μ = 3.95, find the probability that x = 16.
Give the percent of scores between the mean and the z-value of normally distributed random variable. a 1) 1.25
Talent Corp is a HR-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below. Number of New Clients Probability 0 0.05 1 0.10 2 0.15 3 0.30 4 0.25 5 0.10 6 0.05 Compute the expected number of new clients each month. Compute the variance and standard deviation for the expected number of new clients. What is the probability that there will be 2 or fewer clients next month?
Compute the posterior distribution for X.
Response team hears directly from consumers about the challenges they face in the marketplace, brings their concerns to the attention of financial institutions, and assists in addressing their complaints. An analysis of complaints registered recently indicates that the mean number of vehicle lease complaints registered by consumers is 3.5 per day. Assume that the number of vehicle lease complaints registered by consumers is distributed as a Poisson random variable. What is the probability that in a given day d. fewer than two vehicle lease complaints will be registered by consumers?
Oxygen demand is a term biologists use to describe the oxygen needed by fish and other aquatic organisms for survival. The Environmental Protection Agency conducted a study of a wetland area. In this wetland environment, the mean oxygen demand was μ = 9.2 mg/L with 95% of the data ranging from 5.4 mg/L to 13.0 mg/L. Let x be a random variable that represents oxygen demand in this wetland environment. Assume xhas a probability distribution that is approximately normal. (a) Use the 95% data range to estimate the standard deviation for oxygen demand. (b) An oxygen demand below 8 indicates that some organisms in the wetland environment may be dying. What is the probability that the oxygen demand will fall below 8 mg/L?(Round your answer to four decimal places.) (c) A high oxygen demand can also indicate trouble. An oxygen demand above 12 may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed 12…
Oxygen demand is a term biologists use to describe the oxygen needed by fish and other aquatic organisms for survival. The Environmental Protection Agency conducted a study of a wetland area. In this wetland environment, the mean oxygen demand was μ = 9.9 mg/L with 95% of the data ranging from 6.3 mg/L to 13.5 mg/L. Let x be a random variable that represents oxygen demand in this wetland environment. Assume x has a probability distribution that is approximately normal. (a) Use the 95% data range to estimate the standard deviation for oxygen demand. (b) An oxygen demand below 8 indicates that some organisms in the wetland environment may be dying. What is the probability that the oxygen demand will fall below 8 mg/L? (Round your answer to four decimal places.) (c) A high oxygen demand can also indicate trouble. An oxygen demand above 12 may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed 12…
Of the students in the college, 60% of the students reside in the hostel and 40% of the students are day scholars. Previous year result reports that 30% of all students who stay in the hostel scored A Grade and 20% of day scholars scored A grade. At the end of the year, one student is chosen at random and found that he/she has an A grade. What is the probability that the student is a hostlier?
Use the Poisson distribution to find the indicated probabilities Deaths from Horse Kicks A classical example of the Poisson distribution involves the number of deaths caused by horse kicks to men in the Prussian Army between 1875 and 1894. Data for 14 corps were combined for the 20-year period, and the 280 corps-years included a total of 196 deaths. After finding the mean number of deaths per corps-year, find the probability that a randomly selected corps-year has the following numbers of deaths: (a) 0, (b)1, (c)2, (d)3, (e)4. The actual results consisted of these frequencies: 0 deaths (in 144 corps-years) ;1 death (in 91 corps-years); 2 deaths (in 32 corps-years); 3 deaths (in 11 corps-years); 4 deaths (in 2 corps-years). Compare the actual results to those expected by using the Poisson probabilities. Does the Poisson distribution serve as a good tool for predicting the actual results?
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The number of admissions per day at an emergency room has a Poisson distribution and its parameter is 5.Find the probability of I. At least 3 admissions per day II. At most 8 admissions per day.

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