Using 10000 times simulation find the mean variance and the

Question

Q1) For the following cases, write down the likelihood function.

(a) Let Y|θ be Poisson(θ). Suppose that we believe there are only four possible values for θ; 1, 1.5, 2 and 2.5 and y = (1, 2).

(b) Consider the regression model

Y_i = β + X_i + ?_i;     i = 1, 2......., 3

with the observations:

y	x
10	1
11	2
12	3

Q2) For the example 2, suppose Sally has a forth son, who is affected and update your information on θ.

Q3) For the following problems use SAS and R. Attach your programming code and relevant output to the assignment.

(a) Simulate the rolling of a die three times and find the mean, variance, and the distribution of the sum of the three outcomes. Use 10,000 times repetitions in your simulation.

(b) Using 10,000 times simulation, find the mean, variance, and the distribution of the median of a sample of 25 observations from a standard normal distribution.

Attachment:- Chapter Notes.rar