2. Let X, X2,X, be a random sample of size n from an Erp(1/0) distribution (i.e with mean 0 and variance 6). (a) Derive an expression for E(X) and Var(X) in terms of 0 where X is the mean of the random sample. (b) Express MSE(X) in terms of Var(X) and Bias (X) and hence find an expression for MSE(X) in terms of @. (c) Consider the family of estimators for 6 of the form Y = aX. Find MSE(aX) and determine the value of a such that Y = a*X is the most efficient estimator of the form Y = aX.
2. Let X, X2,X, be a random sample of size n from an Erp(1/0) distribution (i.e with mean 0 and variance 6). (a) Derive an expression for E(X) and Var(X) in terms of 0 where X is the mean of the random sample. (b) Express MSE(X) in terms of Var(X) and Bias (X) and hence find an expression for MSE(X) in terms of @. (c) Consider the family of estimators for 6 of the form Y = aX. Find MSE(aX) and determine the value of a such that Y = a*X is the most efficient estimator of the form Y = aX.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Question
please send solution for Q 2
only handwritten solution accepted
![1. The numbers of claims which have arisen in the last twelve years
policies (continuously in force over this period) are shown (sorted) below
60 motor car
000 0 0 0 0 000 0 0 1 1111 1
11111 1 2 22 2 2 2 2 2 2 22 3 3 3
3 333333 444 4 4 5 55 5 6 6 6 7
(a) Draw a barplot of the number of claims.
(b) Calculate the median, mode and mean of the data.
(c) Calculate the interquartile range and the standard deviation of the
data.
2. Let X1, X2, ,X„ be a random sample of size n from an Exp(1/0) distribution (i.e
with mean 6 and variance 62).
(a) Derive an expression for E(X) and Var(X) in terms of 0 where X is the mean of
the random sample.
(b) Express MSE(X) in terms of Var(X) and Bias (X) and hence find an expression
for MSE(X) in terms of .
(c) Consider the family of estimators for 0 of the form Y = aX.
Find MSE(aX) and determine the value of a such that Y = a*X is the most
efficient estimator of the form Y = aX.
[3]
3. Let X1, X2, . X, be a random sample from the probability distribution
;0<I<1
f(x,0) =
otherwise
where the parameter 0 > 0.
(a) Find EX] for this distribution
(b) Use the method of moments (MME) to find an estimator for 0
(c) Find the maximum likelihood estimator (MLE)for 0.
(d) Calculate the estimate using the MME and MLE estimators when
I = 0.10, 12 = 0.22, 13 = 0.54, 1 = 0.36](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbbea9d03-e0eb-4d48-beb5-27420e56a67f%2Fe3d6aab7-7c9b-45c7-9142-a53b45697c78%2Fe0csw4d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. The numbers of claims which have arisen in the last twelve years
policies (continuously in force over this period) are shown (sorted) below
60 motor car
000 0 0 0 0 000 0 0 1 1111 1
11111 1 2 22 2 2 2 2 2 2 22 3 3 3
3 333333 444 4 4 5 55 5 6 6 6 7
(a) Draw a barplot of the number of claims.
(b) Calculate the median, mode and mean of the data.
(c) Calculate the interquartile range and the standard deviation of the
data.
2. Let X1, X2, ,X„ be a random sample of size n from an Exp(1/0) distribution (i.e
with mean 6 and variance 62).
(a) Derive an expression for E(X) and Var(X) in terms of 0 where X is the mean of
the random sample.
(b) Express MSE(X) in terms of Var(X) and Bias (X) and hence find an expression
for MSE(X) in terms of .
(c) Consider the family of estimators for 0 of the form Y = aX.
Find MSE(aX) and determine the value of a such that Y = a*X is the most
efficient estimator of the form Y = aX.
[3]
3. Let X1, X2, . X, be a random sample from the probability distribution
;0<I<1
f(x,0) =
otherwise
where the parameter 0 > 0.
(a) Find EX] for this distribution
(b) Use the method of moments (MME) to find an estimator for 0
(c) Find the maximum likelihood estimator (MLE)for 0.
(d) Calculate the estimate using the MME and MLE estimators when
I = 0.10, 12 = 0.22, 13 = 0.54, 1 = 0.36
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