Find the probability that the test for a pooled sample

Reference no: EM13970286

A large number, N , of people are subjected to a blood test. This can be administered in two ways: (1) Each person can be tested separately, in this case N test are required, (2) the blood samples of k persons can be pooled and analyzed together. If this test is negative, this one test suffices for the k people. If the test is positive, each of the k persons must be tested separately, and in all, k + 1 tests are required for the k people. Assume that the probability p that a test is positive is the same for all people and that these events are independent.

(a) Find the probability that the test for a pooled sample of k people will be positive.

(b) What is the expected value of the number X of tests necessary under plan (2)? (Assume that N is divisible by k.)

(c) For small p, show that the value of k which will minimize the expected number of tests under the second plan is approximately 1/√p.

Reference no: EM13970286

Questions Cloud

What is your estimate for this number : Have your program repeat this experiment a number of times to estimate the expected number of selections necessary in order that the sum of the chosen numbers first exceeds 1. On the basis of your experiments, what is your estimate for this number..

Prepare for a due process hearing in special education : List the steps that need to be taken in preparing for a due process hearing, with short paragraphs explaining why each step is necessary. (You may integrate information developed for previous assignments in this course.)

What expenditures deductible for self-employed individual : What expenditures are deductible for self-employed individuals but are not deductible for employees? Discuss why there would be this distinction.

What questions did bruce not answer to your satisfaction : What questions did Bruce not answer to your satisfaction? (if any) What would you do (or not do!) based upon the post?

Find the probability that the test for a pooled sample : Find the probability that the test for a pooled sample of k people will be positive - what is the expected value of the number X of tests necessary under plan

Spend exploring the websites : While you're reading consider the following questions: What motivates people who are drawn to this philosophy? What are some advantages/what appeals to you? What are some disadvantages/what turns you off?

Spend some time searching the internet for videos : Spend some time searching the Internet for videos/blogs/articles that discuss health care reform in an engaging and non-biased way. This is a very challenging task. (Believe me, I've spent a lot of time trying to find resources for this course!) FIND..

Why is this an optimal strategy : Show that if n ≥ 2k - 1, there is a strategy that assures you of identifying one of 2k - 1 numbers and hence gives a probability of (2k - 1)/n of winning. Why is this an optimal strategy? Illustrate your result in terms of the case n = 9 and k = 3..

When would the accrual method be used, and why : Please select an exclusion from income. Explain the exclusion and its purpose. What do you think the congressional intent was for this exclusion?

User Account

All Pages