Graduate Essay Writers
Only the finest writers are selected to be a part of our team, with each possessing specialized knowledge in specific subjects and a background in academic writing..
Fill the order form in 3 easy steps - Less than 5 mins.
Posted: April 10th, 2022
Solutions to all questions needs to be handed in to the postbox within the statistics hall by 2pm on
Thursday 25st January. Please bear in mind to fill the task kind in all of the required
elements. Yow will discover the shape within the Statistics hall.
• Suppose that X¯ = (X1, . . . , Xn) are i.i.d. steady random variables with p.d.f. given by
f1,θ(x) = (θ + 1)x
θ1(zero,1)(x)
for θ > −1.
(i) Describe the statistical mannequin. [2 marks]
(ii) Assemble the chance and plot it for values n = three and x = (.2, .6, .1). [4 marks]
(iii) Assemble the Maximum Likelihood Estimate ˆθ(x1, . . . , xn). [4 marks]
(iv) Compute the imply of the Maximum Likelihood Estimator (MLE). What occurs? [2 marks]
(v) Suppose that we don’t need to estimate θ however a functiont of θ given by
ζ(θ) = θ + 1
θ + 2
.
We use the estimator
ˆζ(X1, . . . , Xn) = 1
n
Xn
x=1
Xi
.
Is that this an unbiased estimator? Compute the variance and Imply Sq. Error. [4 marks]
(vi) From Theorem 2 of part 9.2 of the textbook, we will instantly derive that the MLE for
parameter ζ is given by
ˆζMLE(X1, . . . , Xn) =
ˆθ(X1, . . . , Xn) + 1
ˆθ(X1, . . . , Xn) + 2
= 1 −
1
ˆθ(X1, . . . , Xn) + 2
.
Evaluate the 2 estimators ˆζ and ˆζMLE, for n = 1. [4 marks]
Every Student Wants Quality and That’s What We Deliver
Only the finest writers are selected to be a part of our team, with each possessing specialized knowledge in specific subjects and a background in academic writing..
We balance affordability with exceptional writing standards by offering student-friendly prices that are competitive and reasonable compared to other writing services.
We write all our papers from scratch thus 0% similarity index. We scan every final draft before submitting it to a customer.
When you opt to place an order with Nursing StudyBay, here is what happens:
Place an order in 3 easy steps. Takes less than 5 mins.