A river where drinking water is taken is feared to have been polluted by coliformbacteria In order to investigate this, we take a sample tube of water at n randomlyselected sites from the river tube and from each of these samples we determine thenumbers of coliform bacteria y₁, ..., Yn.A classical distribution used to describe the distribution of the number of bacteriaper unit volume of water, is the Poisson distribution. So we model our measurementresults so that they form a random sample Y₁,..., Yn from Poisson distribution, i.e.we assume we have n independent observations from the Poisson distribution.(a) Construct the likelihood function L(\; y) of the model and construct the log-likelihood function ((\; y) of the model(b) Derive by examining the log-likelihood function and carefully justifying the max-imum likelihood estimate of the parameter(c) Show with justifications that the ML estimator of the model is unbiased(d) Calculate the mean squared error msex (^(Y)) of the ML estimator of the model

The probability density function of the Poisson distribution is given as: where y=0,1,2,...

Answered: A river where drinking water is taken…

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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Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.78. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.9 4.2 4.5 4.1 4.4 4.3 (i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x = s = (ii) Do the given data indicate that the population mean RBC count for this patient is lower than 4.78? Use ? = 0.05. (a) What is the level of significance?State the null and alternate hypotheses. H0: ? < 4.78; H1: ? = 4.78H0: ? = 4.78; H1: ? ≠ 4.78 H0: ? = 4.78; H1: ? < 4.78H0: ? = 4.78; H1: ? > 4.78H0: ? > 4.78; H1: ? = 4.78 (b) What sampling…
The two data sets in the table below are dependent random samples. The population of (x - y) differences is approximately normally distributed. A claim is made that the mean difference (x - y) is less than 29.3. X y DII For each part below, enter only a numeric value in the answer box. For example, do not type "z =" or "t=" before your answers. Round each of your answers to 3 places after the decimal point. (a) Calculate the value of the test statistic used in this test. Test statistic's value = -2.760 61 71 58 48 38 41 (b) Use your calculator to find the P-value of this test. P-value $ 4 44 48 66 43 32 30 29 33 (c) Use your calculator to find the critical value(s) used to test this claim at the 0.07 significance level. If there are two critical values, then list them both with a comma between them. Critical value(s) = -1.700 (d) What is the correct conclusion of this hypothesis test at the 0.07 significance level? O There is sufficient evidence to support the claim that the mean…
The frequency distribution table below is the net weight of a sample of candied fruit products in the food industry cans "ABC": - How many cans have a net weight of less than 20.2 grams. - If we want to compare about the distribution of net weight with the food company "XYZ" for the same type of product. And it is known that the average and variance is 20 grams and 0.04 grams. Which food company has an even distribution of net weight.
We have a Poisson distribution for cacti with a mean of 280 per square kilometer. They are asking for the mean of cacti per 10,000 square meters. They are telling us that 1 square kilometer = 1,000,000 square meters. My confusion is on converting the units. When they say 280 per square kilometer, are they saying 280 divided by square kilometer? I've attached an image of my work. My professor said that the answer is 2.8.
tion w E Bb Collaborate - 2020 Fall Term + ed.cuny.edu/webapps/assessment/take/launch.jsp?course_assessment_id=_1729781_1&course_id%3 1968349 1&content id- 53765765 18step=null * Question Completion Status: QUESTION 1 A graphical display of a data set is given. Identify the overall shape of the distribution as (roughly) bell-shaped, triangular, uniform, reverse J-shaped, J-shaped, right skewed, left skewed, bimodal, or multimodal. 1 pc A relative frequency histogram for the sale prices of homes sold in one city during 2006 is shown below. Relative Frequency 0.35 0.30- 0,25 0.20 0.15 0.10 0.05 - 0.00 10 15 20 25 30 35 40 45 Sale price of home ($10,000s) Solution: Right skewed O J-shaped O Right skewed O Left skewed O Reverse J-shaped
My question for my stats homework comes from the textbook Introduction to the Practice of Statistics Ninth Edition. This comes from section exercise 1.80. from the textbook, my professor wants me to caluate using the three columns. Can you help me slove this problem for me?
Researchers wanted to determine if carpeted rooms contained more bacteria than uncarpeted rooms. To determine the amount of bacteria in a room, researchers pumped the air from the room over a Petri dish at the rate of 1 cubic foot per minute for eight carpeted rooms and eight uncarpeted rooms. Colonies of bacteria were allowed to form in the 16 Petri dishes. The results are given in the table below. Assume the distribution to be approximately normal. Do carpeted rooms have more bacteria than uncarpeted rooms? Carpeted Rooms Uncarpeted Rooms 11.7 12.0 8.2 8.3 7.1 3.8 13.1 7.3 10.6 12.0 10.1 11.1 14.8 10.3 14.0 13.7 What is the critical value(s) for this hypothesis test if group 1 is the carpeted rooms and group 2 is the uncarpeted rooms. 1.895 2.306 2.365 1.833 1.860
What is the difference between the t and z distributions? Which is used more in biological research? Explain your anwser.

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