Q1: Suppose the number of customers X that enter a store between the hours 9:00 a.m. and10:00 a.m. follows a Poisson distribution with parameter 0. Suppose a random sample ofthe number of customers that enter the store between 9:00 a.m. and 10:00 a.m. for 10 daysresults in the values9, 7, 9, 15, 10, 13, 11, 7, 2, 12Determine the maximum likelihood estimate of 0. Show that it is an unbiased estimator.Q2: Assume that X is a discrete random variable with pmf f(x). Let X₁,...,X₁ be a randomsample on X. Suppose that the space of X is finite, say, D={a₁,...,m}. An intuitiveestimate of p(a) is the relative frequency of a, in the sample. We express this moreformally as follows. For j=1, 2,..., m, define the statistics1,(X) = {1 0X₁ = a;X₁ = a;Then the intuitive estimate of p(a)) can be expressed by the sample averagep(a) = -1,(X₂)Find the unbiased estimator and the variance of the estimator and its mgf.

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Answered: Q1: Suppose the number of customers X…

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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Assume that the amount of weight that male college students gain during their freshman year are normally distributed with a. Mean of u= 1.2 kg and a standard deviation of o= 5.1 kg A. If 1 male college student is randomly selected, Find the probability that he gains between 0 and 3 kg during freshman year B. If 25 male college students are randomly selected find the probability that their mean weight gain during freshman year is between 0 and 3 kg why can the normal distribution be used on pet b even though the sample size does not exceed 30?
In a random sample of sixteen different industries the percentage employment x in construction and mean annual compensation y were recorded, with the following results (in the file). y-hat = 1.1527x + 741.9797 1) Give a point estimate for the increase in mean annual compensation of workers in any industry for each additional percentage point increase in the percentage of workers in construction.
E The number of accidents occurring in a plant in a month follows Poisson distribution with mean as 5.2. The probability of occurrence of less than 2 accidents in the plant during a randomly selected month is
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A randomly selected group of 560 students are assumed to have heights distributed normally with meanµ = 166 cm and standard deviation σ = 30 cm. Suppose a student is chosen randomly from this group. Finda. the probability that this student’s height is between 170 cm and 182 cm.b. the probability that this student’s height is bigger than 175 cm.
The number of hours in a month a sample of 12 people chosen at random from a normal population work is as follows: 55,55,54,56,56,58,60,62,61,59,59,60. Can we conclude that the mean of the sample differs significantly from the assumed population average of 56 hours? Given that t11,0.05  2.201.
The number of accidents per day has the poisson distribution where the value of mean is 0.8. Determine: (i)The number of accidents within eight days that are selected at random.(ii)The probability that at least three accidents happened within eight days that are selected at random.(iii)The probability that less thank four accidents happen within twelve days that are selected at random.
The ground-up losses have an exponential distribution with mean 750,000. A deductible of 500,000 is applied to the product and the frequency distribution for the total number of losses, , is Poisson with mean 2. What is the percentage of policyholders be expected to have at least one claim paid to them?
Let a population consist of the values 11 cigarettes, 12 cigarettes, and 22 cigarettes smoked in a day. Show that when samples of size 2 are randomly selected with replacement, the samples have mean absolute deviations that do not center about the value of the mean absolute deviation of the population. What does this indicate about a sample mean absolute deviation being used as an estimator of the mean absolute deviation of a population? Calculate the mean absolute deviation for each possible sample of size 2 from the population. Mean Absolute Deviation Sample {11,11} {11,12} {11,22} {12,11} {12,12} {12,22} {22,11} {22,12} {22,22} (Type integers or decimals rounded to one decimal place as needed.) Budget Pi nd Pow....P Enter your answer in the edit fields and then click Check Answer. Clear All Check Answer parts
Now suppose that the manufacturing company specializing in semiconductor chips follows a Poisson distribution with an average output of 10,000 chips per day. Approximate the expected number of days in a year that the company produces more than 10,200 chips in one day. It is requested that:to. State the solution with the original formula of the distribution, explaining why you consider that distribution to be and explaining in detail what I did (do not solve the equation)b. Solve the exercise by performing the respective normal approximation, explaining step by step how and why you do it
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