prediction: Consider

Posterior prediction: Consider a pilot study in which n1 = 15 children enrolled in special education classes were randomly selected and tested for a certain type of learning disability. In the pilot s

Posterior prediction: Consider a pilot study in which n1 = 15 children

enrolled in special education classes were randomly selected and tested for a certain type of learning disability. In the pilot study, y1 = 2 children tested positive for the disability.

a) Using a uniform prior distribution, find the posterior distribution of θ, the fraction of students in special education classes who have the disability. Find the posterior mean, mode and standard deviation of θ, and plot the posterior density.

Researchers would like to recruit students with the disability to participate in a long-term study, but first they need to make sure they can recruit enough students. Let n2 = 278 be the number of children in special edu- cation classes in this particular school district, and let Y2 be the number of students with the disability.

b) Find Pr(Y2 = y2|Y1 = 2), the posterior predictive distribution of Y2, as follows:

Discuss what assumptions are needed about the joint distribution of (Y1,Y2) such that the following is true:

1 0

Now plug in the forms for Pr(Y2 = y2|θ) and p(θ|Y1 = 2) in the above integral.

Pr(Y2 = y2|Y1 = 2) =

Pr(Y2 = y2|θ)p(θ|Y1 = 2) dθ .

iii. Figure out what the above integral must be by using the calculus result discussed in Section 3.1.

c) Plot the function Pr(Y2 = y2|Y1 = 2) as a function of y2. Obtain the mean and standard deviation of Y2, given Y1 = 2.

Scroll Below to View Our Previous Reviews

Calculate the price of your order

Continue with Order
Continue with Order
Continue with Order
Continue with Order

Simple Order Process

Fill in the Order Form

Share all the assignment information. Including the instructions, provided reading materials, grading rubric, number of pages, the required formatting, deadline, and your academic level. Provide any information and announcements shared by the professor. Choose your preferred writer if you have one.

Get Your Order Assigned

Once we receive your order form, we will select the best writer from our pool of experts to fit your assignment.

Share More Data if Needed

You will receive a confirmation email when a writer has been assigned your task. The writer may contact you if they need any additional information or clarifications regarding your task

Let Our Essay Writer Do Their Job

Once you entrust us with your academic task, our skilled writers embark on creating your paper entirely from the ground up. Through rigorous research and unwavering commitment to your guidelines, our experts meticulously craft every aspect of your paper. Our process ensures that your essay is not only original but also aligned with your specific requirements, making certain that the final piece surpasses your expectations.

Quality Checks and Proofreading

Upon the completion of your paper, it undergoes a meticulous review by our dedicated Quality and Proofreading department. This crucial step ensures not only the originality of the content but also its alignment with the highest academic standards. Our seasoned experts conduct thorough checks, meticulously examining every facet of your paper, including grammar, structure, coherence, and proper citation. This comprehensive review process guarantees that the final product you receive not only meets our stringent quality benchmarks but also reflects your dedication to academic excellence.

Review and Download the Final Draft

If you find that any part of the paper does not meet the initial instructions, send it back to us with your feedback, and we will make the necessary adjustments.