37357留学生讲解、讲解Statistical Modelling、辅导Python，c++编程、Java程序语言辅导解析R语言编程|讲解D

37357 Spring 2019 Page 1 of 5
37357 Advanced Statistical Modelling
Lab Week 4
Distribution Theory and MLE
Name: Student Number:
Part 1: Poisson Distribution
Let Y1, …, Yn be independent random variables that follow the Poisson distribution
(1) Write down the likelihood function,
(2) Write down the log-likelihood function.37357 Spring 2019 Page 2 of 5
(3) Calculate
(4) Find the maximum likelihood estimator of.
Part 2: Unbiased Estimators
Let Yi = μ + εi, i=1,…,n with independent and identically distributed errors εi such that E[εi] = 0 and
Var[εi] = σ2
.
(5) Find the least squares estimator of μ.
Part 3: Binomial Distribution
Let Y be a random variable that follows the Binomial distribution
(7) Write down the likelihood function,37357 Spring 2019 Page 4 of 5
(8) Write down the log-likelihood function,
(10) Find the maximum likelihood estimator of.
Open the Excel sheet “MLE Bin Dist.xlsx” on UTSOnline. This sheet calculates based on n = 30
Bernoulli trials both algebraically (the MLE found in Q10) and numerically (by finding the maximum
likelihood from a list of possibilities). You can re-run the trails by pressing F9.
(11) Leave the “true p” at 0.3 and re-run the trails 10 times. Each time you re-run the trials, write
down . Do to algebraic and numeric estimates of p agree with one another in each re-run?37357 Spring 2019 Page 5 of 5
(12) Calculate the mean and standard deviation of the 10 estimates of p in the previous question.
What do you think will happen to the mean and standard deviation when n is larger?
(13) Increase n from 30 to 60 by creating 30 more trials in Row 7. You can do this by copying the
contents of row 6 from column E to AH. Check that the calculation of n in the top left corner has
changed. Repeat question 11 with the increased sample size.
(14) Increase n from 60 to 90 by creating 30 more trials in Row 8. Repeat question 11 with the
increased sample size.
(15) Calculate the mean and standard deviation of the estimates of p in each of Q13 and Q14.
Comment on the effect of increasing n.
More fun things to play with: change the value of “true p”.

37357留学生讲解、讲解Statistical Modelling、辅导Python，c++编程、Java程序语言辅导 解析R语言编程|讲解D

37357留学生讲解、讲解Statistical Modelling、辅导Python，c++编程、Java程序语言辅导解析R语言编程|讲解D