Purchase Solution

Observed and expected frequencies

Not what you're looking for?

Ask Custom Question

Please see the attached file for full problem description.

---
? 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.

Attachments
Purchase this Solution
Solution Summary

This shows how to find the maximum likelihood estimate of the mean of a Poisson distribution, and estimate the expected frequencies corresponding to observed frequencies.

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Probability Quiz

Some questions on probability

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

View More Free Quizzes
Related BrainMass Solutions

  • Statistics: Chi-square

    TRUE In this case, as the difference between the respective observed and expected frequencies decrease, the value of the 2 is getting smaller and smaller.

  • Chi square test

    C.for each row and column, the sum of the observed frequencies and the sum of the expected frequencies come out to be the same.

  • Multiple choice questions from Chi-Square test

    the expected frequencies are consistently larger than the observed frequencies there are large differences between the observed and expected frequencies 8.

  • Chi-square Test of Goodness of Fit

    The test Statistic used is where O is the observed frequency and E is the expected frequency. The Observed and Expected frequencies are given below.

  • Certainty independent of credits earned

    Test Statistics: Where o ij is the observed frequencies and the e ij is the expected frequencies Table for computing the test statistics: Observed Expected (O-E) (O-E)^2 ((O-E)^2)/E 12 7.5 4.5 20.25 2.7 8 6.8 1.2 1.44 0.211765

  • ChiSquare test for goodness of fit

    H0: There is no significant difference in the expected and observed frequencies. H1: There is significant difference in the expected and observed frequencies.

  • Chi-square Test for Goodness of Fit

    These numbers are the observed frequencies for each of the categories A, B, C, and D for our sample of 580 correct answers.

  • Poisson distribution

    Comment informally on the extent of agreement between these observed and expected frequencies.

  • Expected Frequency

    Problem 1c 21 25 15 10 13 10 11 45 27 Answer The observed and expected frequencies are given below.

View More Related Solutions