binomial random variable Expectation
Each of 1000 people in a place independently has a certain
disease with probability 0.005.
The disease can be show up in the blood test by two methods
Method 1- Each person has separate test
Method 2- Ten groups of 100 people are formed. The blood samples of 100 people in a group are mixed and later tested. Given that test is positive, implying that at least one person in the group has the disease, all 100 people must be tested separately. We do this for all the ten groups.
(i). What is the expected number of blood tests performed for the 1000 people in method 1? Is it 0.005 x 1000=5
(ii)In method 2, if y is the number of blood tests performed in a single group of 100 people, what is the expected value of y?