# Help calculating expected value (i'm not sure which distribution this is)

• Oct 4th 2009, 05:18 PM
Intsecxtanx
Help calculating expected value (i'm not sure which distribution this is)
In group testing for a certain rare virus, a blood sample is taken from each of n individuals, and part of each sample is placed in a common pool. If the result on the pool is negative, no further testing would be needed. If the combined result is positive, each individual sample is tested, requiring in total n + 1 tests. If the virus is present in an individual blood sample with probability 5%, and n = 10, compute the expected number of tests needed (assume independence).

Any help with this problem is really appreciated. thank you.
• Oct 5th 2009, 01:45 PM
CaptainBlack
Quote:

Originally Posted by Intsecxtanx
In group testing for a certain rare virus, a blood sample is taken from each of n individuals, and part of each sample is placed in a common pool. If the result on the pool is negative, no further testing would be needed. If the combined result is positive, each individual sample is tested, requiring in total n + 1 tests. If the virus is present in an individual blood sample with probability 5%, and n = 10, compute the expected number of tests needed (assume independence).

Any help with this problem is really appreciated. thank you.

With probability $\displaystyle 0.95$ $\displaystyle 1$ test is required and with probability $\displaystyle 0.05$ $\displaystyle n+1$ tests are required.

Therefore the expected number of tests:

$\displaystyle E(N)=0.95 \times 1 + 0.05 \times (n+1)$

CB