Cashback Offer from 16th to 19th October 2021. Get Flat 10% Cashback credited to your account for a minimum transaction of \$80. Post Your Question Today!

Question DetailsNormal
\$ 25.00

# STAT 400 Homework #9 | q2-q5 Solution

Question posted by  2. Let X 1 , X 2 , … , X n be a random sample of size n from the distribution with
probability density function
f ( x ; λ ) =
λ 2 2 λ e− x
π
, x > 0, λ > 0.
a) Obtain the maximum likelihood estimator of λ, λˆ .
d) Suppose n = 4, and x 1 = 0.2, x 2 = 0.6, x 3 = 1.1, x 4 = 1.7.
Find the maximum likelihood estimate of λ.
c) Obtain the method of moments estimator of λ, λ
~
.
d) Suppose n = 4, and x 1 = 0.2, x 2 = 0.6, x 3 = 1.1, x 4 = 1.7.

Find a method of moments estimate of λ.
3. Let X 1 , X 2 , … , X n be a random sample from the distribution with probability
density function
( ) ( ) ( ) ( )
X X θ 2 1 1
f x = f x; = θ + θ x θ − − x , 0 < x < 1, θ > 0.
a) Obtain the method of moments estimator of θ, θ ~
.
b) Is θ ~
c) Suppose n = 6, and x 1 = 0.3, x 2 = 0.5, x 3 = 0.6, x 4 = 0.65, x 5 = 0.75, x 6 = 0.8.
Find a method of moments estimate of θ.

4. Let θ > 0 and let X 1 , X 2 , … , X n be a random sample from a Uniform distribution
on interval ( 0, θ ).
a) Obtain the method of moments estimator of θ, θ ~
.
b) Is θ ~
c) Find Var ( θ ~ ). d) Find MSE ( θ ~ ).

5. Let X 1 , X 2 , … , X n be a random sample from the distribution with probability
density function
( ) θ
;θ θ
12 8
3
+
+
=
f x x , 0 < x < 4, θ >
4
3
− .
a) Find the method of moments estimator of θ, θ ~
.
b) Suppose n = 5, and x 1 = 1.2, x 2 = 1.8, x 3 = 2.6, x 4 = 3.1, x 5 = 3.8.
Find the method of moments estimate of θ.
c) Suppose n = 4, and x 1 = 1.3, x 2 = 2.2, x 3 = 3.1, x 4 = 3.8.
Find the method of moments estimate of θ.

\$ 25.00

## [Solved] STAT 400 Homework #9 | q2-q5 Solution

• This Solution has been Purchased 1 time
• Average Rating for this solution is A+
• Submitted On 11 Apr, 2015 01:18:31  (X)=∫_0^1▒〖x f(x)dx〗 =∫_0^1▒〖x (theta^2+theta) x^(theta-1) (1-x)dx〗 =(theta^2+theta) ∫_0^1▒〖x...
Buy now to view the complete solution Other Similar Questions smart...

### STAT 400 Homework #9 | q2-q5 Solution

(X)=∫_0^1▒〖x f(x)dx〗 =∫_0^1▒〖x (theta^2+theta) x^(theta-1) (1-x)dx〗 =(theta^2+theta) ∫_0^1▒〖x^theta (1-x)dx〗 =(theta^2+theta) ∫_0^1▒〖x^theta-x^(theta+1) dx〗 =(theta^2+theta) (x^(theta+1)/(theta... Exper...

### STAT 400 Homework 8 | Complete solution

This Tutorial is rated A+ previously,if you have any questions regarding this tutorial then you can contact me....

#### The benefits of buying study notes from CourseMerit ##### Assurance Of Timely Delivery
We value your patience, and to ensure you always receive your homework help within the promised time, our dedicated team of tutors begins their work as soon as the request arrives. ##### Best Price In The Market
All the services that are available on our page cost only a nominal amount of money. In fact, the prices are lower than the industry standards. You can always expect value for money from us.  