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Consider a random sample of size n from a Poisson distribution, Xi ~ POI(m).
a) Find the CRLB for the variances of unbiased estimators of m.
b) Find the CRLB for the variances of unbiased estimators of theta = e^(-m).
c) Find the UMVUE of m.
d) Find the MLE theta(hat) of theta.
e) Is theta(hat) an unbiased estimator of theta?
f) Is theta(hat) asymptotically unbiased?
g) Show that theta~ = [(n-1)/n]^(sum Xi) is an unbiased estimator of theta.
h) Find Var(theta~) and compare to the CRLB of b).
Problem based on decision tree - Evaluate the strategy that maximizes the manufacturer's expected net earnings.
Height of men have a mean of 69.6 inches and standard Dev of 2.8 inches. If 64 men are randomly seleted, find the probabilty that they have a mean greater than 70.6 inches.
1. for the 16 teams in the national league data is shown for the team batting averages as of august 27 2012.
A director of an agency is hiring temporary help. In making plans, he has to know whether there isi any difference in the use of the agency at different seasons of the year.
Parameter of interest is mean score in this population. Sample is an SRS of size n = 4 drawn from population. Determine the mean of 10 scores in the population.
How does the percentage likelihood of a successful negotiation change over the course of time? Use the statistical data to inform the plan and the course of action the department will take in this hostage situation.
Mean of 29.44 with a standard deviation of 2.86. Conduct a two tailed hypothesis test at a significance level of .05 to see if the two means are different.
Is there sufficient evidence at the alpha =0.05 level to support the researcher's claim?
A company's manufacturing process uses 500 gallons of water at a time. A "scrubbing" machine then removes most of a chemical pollutant before pumping the water into a nearby lake. To meet federal gregulations the treated water must not contain more t..
1) There are 500 employees in a firm, 45% are female. A sample of 60 employees is selected randomly. a) Determine the standard error of the proportion.
Two men are carrying a girl on a large plank that is 10m long and weights 200N. If the girl on a plank weighs 445N and sits 3m from one end, how much weight must each man support?
A researcher used stepwise regression to create regression models to predict Birth Rate (births per 1,000) using five predictors: Life Exp (life expectancy in years).
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