p.d.f.of Geometric Distribution is given by:
,
for x = 1, 2,...
The mean of geometric distribution is given by:
,
since
Thus, we get:
(1)
Given:
Independent r.v.'s: X1, X2,...,Xn.
So,
Mean is given by:
(2)
Equating (1) & (2), we get:
Thus, the moment estimate of
is given by:
.
This is same as MLE of
5.1 Refer to Exercise 1.6, and derive the moment estimate of θ. Also, compare it with...
5.3 Refer to Exercise 1.8, and derive the moment estimate of θ.
,nbe a rardom sample uiorm d tribution with pa 3D +2 Otherwi se (a) Please derive the mełthod moment esbima tor (MOME) θ , please also derive the mean e this (MUME). please derive the metho ) pleause desive the maximum Uxathvol estimator (MLE) el θ. please also derive the meaun d this MLE.
,nbe a rardom sample uiorm d tribution with pa 3D +2 Otherwi se (a) Please derive the mełthod moment esbima tor (MOME) θ , please also...
Using Rstudio to this question. Begin with
set.seed(38257890)
For each of the following simulation studies, please try two different sample sizes (n 30 and n 300). When comparing the estimators, you need to consider both of the bias and variance of the estimates across 100 simulated samples with the same sizes. Please choose your own parameter(s) for the distributions 1. Conduct a simulation study to compare the method of moment estimator and MLE for the parameters of a Beta distribution...
For each of the following simulation studies, please try two different sample sizes (n = 30 and n = 300). When comparing the estimators, you need to consider both of the bias and variance of the estimates across 100 simulated samples with the same sizes. Please choose your own parameter(s) for the distributions. 1. Conduct a simulation study to compare the method of moment estimator and MLE for the parameters of a Beta distribution or Gamma distribution. (You only need...
For each of the following simulation studies, please try two different sample sizes (n = 30 and n = 300). When comparing the estimators, you need to consider both of the bias and variance of the estimates across 100 simulated samples with the same sizes. Please choose your own parameter(s) for the distributions. 1. Conduct a simulation study to compare the method of moment estimator and MLE for the parameters of a Beta distribution or Gamma distribution. (You only need...
Problem 26, please.
303 /629 | (-) (+) | 139% | II are taken. The X2 (i-1,2) are independent of each other, and also of the XI(i 1,2). (The four observations are taken from different components.) It is decided that a reasonable noninformative prior for the situation is Find reasonable Bayesian estimates of o, and e 25. Find the 100(1-α)% HPD credible set in Exercise (a) 7, (b) 11, 12(c), (d) 14 (when 2,-., x, -I. (e) 15(a) (when n...
1. Exercise 5.1 The forecasting staff for the Prizer Corporation has developed a model to predict sales of its air-cushioned-ride snowmobiles. The model specifies that sales, S, vary jointly with disposable personal income, Y, and the population between ages 15 and 40,Z, and inversely with the price of the snowmobiles, P. Based on past data, the best estimate of this relationship is: where k has been estimated (from past data) to equal 100 If Y $13,000, Z- $1,200, and P...
Confidence Interval about a Population Standard Deviation 3) Consider the same information as in Example 2 on page 336, section 7.3, but use a confidence level of 90% instead of 95% Write your solution just like in the example. Show all work and use the formulas (do not use any technology here!) Note that the solution shown in the example is quite detailed. Your solution could be shorter, start where it says Using Table A-4 on page 337, and continue...
X Part I. Derive Bivariate Regression by hand. Again, we are using the same data set that we used in the in-class assessment. Case Dietary Fat Body Fat 22 9.8 22 11.7 14 8.0 21 9.7 32 10.9 26 7.8 30 21 17 1. Step 1: Find the mean of dietary fat x = 2. Step 2: Find the mean of body fat y = 3. Step 3: Find the sum of (x1 - x)y- y) = 3316 4. Step...
eBook Video Exercise 10.1 (Algorithmic)) Consider the following results for two independent random samples taken from two populations. Sample 1 Sample 2 n 50 n2 35 1-1=13.6 X2= 11.1 a. What is the point estimate of the difference between the two population means? | b. Provide a 90% confidence interval for the difference between the two population means (to 2 decimals). c Provide a 95% confidence interval for the difference between the two population means to 2 decimals eBook Video...