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A sample of n independent observations are obtained of a random variable having a Poisson distribution with mean . Show that the maximum likelihood estimate of is he sample mean show that the corresponding estimator is an unbiased estimator of , and has variance .
The scientists Rutherford and Geiger reported an experiment in which they counted the number of alpha particles emitted from a radioactive source during intervals of 7.5 seconds duration, for 2612 different intervals. A total of 10126 particles were counted. The data obtained are summarised in the below.
Number 0 1 2 3 4 5 6 7 8 9 10 11 12 >12 Total
Frequency 57 203 383 525 532 408 273 139 49 27 10 4 2 0 2612
It has been suggested that the number of particles emitted in a n interval may be adequately modelled by a Poisson distribution. Assuming this conjecture to be correct, find the maximum likelihood estimate of the mean of this distribution, and use this to estimate the expected frequencies corresponding to the observed frequencies given in the table. Comment informally on the extent of agreement between these observed and expected frequencies.
Attachment:- statistics 1.doc
the table summarizes data on smoking status and perceived risk of smoking and is consistent with summary quantities
imagine that there are 100 different researchers each studying the sleeping habits of college freshmen. each researcher
Based on your estimate of Equation #1, does experience have an impact on wages - can you improve upon this model? If yes, what does your new model tell you about the impact of experience on wages?
an examination is conducted entirely by multiple choice questions. there are 100 questions and 3 answers are shown for
would changing the asset definition in the conceptual framework to one concerned with property rights have any other
Suppose that in a hypothesis test with null hypothesis = 13.0 at 0.05, that a value of 11.0 for the sample mean results in the null hypothesis not being rejected.
Construct a frequency distribution of the sample mean, and plot a histogram of this distribution. Use the central limit theorem to calculate and identify the sampling distribution of the sample mean.
Simulate arrival of cars at service station for one hour using different stream of random numbers from those used in (a), and calculate average time between arrivals.
for the following situation find the mean and standard deviation of the population. list all samples with replacement
You are the member of the marketing team at Sara Bellum's Pizza - the pizza for people who think too much!! Your mission is to evaluate two locations and determine if there is any difference in their suitability as locations for the next Sara Bell..
Define in words the random variable X. Which distribution should you use for this problem? Why? Construct a 95% confidence interval for the population mean length of engineering conferences.
You have to determine that your cutoff value at level a = 0.05 is 1.645 when testing whether the mean of a population is significantly different from 1.5. If you calculate a test statistic of 1.8 what is the proper conclusion?
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