I need both parts a and b answered. Thank you 5. Expectation of sum is sum of ex

Question

I need both parts a and b answered. Thank you

5. Expectation of sum is sum of expectations: The concept of "pooled screening" of samples is extremely important in settings such as blood banks. Let us consider a concrete example. In a massive blood drive, 1000 people donated blood. These 1000 samples are divided in 100 groups each consisting of 10 samples. The following is then performed 1. For each group of 10 donations, small amounts from each of the 10 donations are pooled together and tested for disease. 2. If the pooled sample comes out to be positive for the disease then every one of the 10 donations are tested for the disease. Thus in this case, a total of 11 tests need to be carried out for that particular group (1 for the pooled test and then 10 individual tests) Page 3 3. The above step is carried out for each of the 100 groups. Suppose each person who donated blood has the disease with probability 0.05 (independent a) 1 point Let Y denote the total number of tests carried over the 100 groups. Find (b)1 point|Suppose every test that is carried out costs the blood bank S78. Let C denote between different people) E(Y). Round to 4 decimal places. the total cost incurred by the blood bank in carrying out the above testing procedure. Find E(C)

Explanation / Answer

here probability that one sample test postive =P(at least one of the person has diseae) =1-P( none has disease)

=1-(1-0.05)10 =0.401263

therefore expected number of a test for a pooled sample =11*P( pooled test comes posiitve)+1*P(pooled test comes negative) = 11*0.401263+1*(1-0.401263)=5.0126

hence expected numebr of test for 100 groups E(Y) =100*5.0126=501.26~ 501

b)

total cost incurred C=78Y

hence expected cost E(C) =78*E(Y) =78*501.26=$39098.5

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.