Let xy X2 ..., Xn be a random sample from a Poisson distribution with parameter A. Find ML estimator of A. Also find its variance.
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A: Answer is explained below
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A: It is an important part of statistics. It is widely used.
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A: As per bartleby guidelines we can solve only first question and rest can be reposted
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- If independent random variables 'X' and 'Y' have the variances 36 and 16 respectively, find the correlation coefficient between (X + Y) and (X- Y) assuming X and Y are zero mean.Let Y₁, Y2, ..., Yn be a random sample from a population with a Gamma distribution with parameters a = 3 and unknown. Find the Minimum Variance Unbiased Estimator for B. Show your work, and explain how you know your estimator is the MVUE.Let X1,...,Xn be a sample from normal with mean theta and variance 1. Construct an unbiased estimator of theta^2 based from X^2. Find its variance and compare it with the Cramer-Rao lower bound.
- A sample of 100 grade 10 students age was obtained to estimate the mean of all grade 10 students. Given x = 15.3 years and the population variance is 162. The average zone of inhibition (in mm) for mouthwash L as tested by the medical technology students has been known to be 9mm. A random sample of 10 mouthwash L was tested and the test yielded an average zone of inhibition of 7.5mm with a variance of 25 mm. Is there enough reason to believe that the anti-bacterial property of the mouthwash has decreased? Test the hypothesis that the average zone of inhibition of the mouthwash is no less than 9mm using 0.05 level of significance. A. State the hypotheses. B. Determine the test statistic to use. C. Determine the level of significance, critical value, and the decision rule. D. Compute the value of the test statistic. E. Make a decision. F. Draw a conclusion.Assume that the population consists of only these eleven data points for y and z. Construct one sample for y and one another sample for z by using 5 data points which gives the maximum variance.If you still have some time, you can add your reviews about the contribution of Bessel’s Correction to the variance. Why do we use such correction and can the variance of any possible sample be larger than the variance of the population?
- Suppose that average male weight in the US is 175 pounds with a standarddeviation of 25 pounds. Suppose you randomly select 1,000 male Americans and ask their weight, and average the 1,000 numbers to compute a sample mean Xn. What is the variance of the sample mean Xn?Suppose that the number of customer that enter a bank in an hour is a Poisson random variable, and suppose that P(X=0)=0.05. Determine the variance of X.A light bulb manufacturer wants to compare the mean lifetimes of two of its light bulbs, model A and model B. Independent random samples of the two models were taken. Analysis of 15 bulbs of model A showed a mean lifetime of 1279 hours and a standard deviation of 100 hours. Analysis of 16 bulbs of model B showed a mean lifetime of 1278 hours and a standard deviation of 88 hours. Assume that the populations of lifetimes for each model are normally distributed and that the variances of these populations are equal. Construct a 99% confidence interval for the difference −μ1μ2 between the mean lifetime μ1 of model A bulbs and the mean lifetime μ2 of model B bulbs. Then find the lower limit and upper limit of the 99% confidence interval. Carry your intermediate computations to at least three decimal places. Round your responses to at least two decimal places.