The number of mutations per strand of DNA for a simple organism has a Poisson di
ID: 3359390 • Letter: T
Question
The number of mutations per strand of DNA for a simple organism has a Poisson distribution with a mean of 1. (a) Suppose a Geneticist randomly collects three non-overlapping strands of DNA from the organism. What is the probability that she will find a total of at least 2 mutations (combining all three strands)? (b) In order for the batch to have any use, she must find at least 2 mutations in the three randomly collected DNA strands (in total). She decides to collect 4 “batches” of the three DNA strands. If the batches were collected independently of each other, what’s the probability that at most 1 of them (the batches) will be useful? How many batches (of three DNA strands) do we expect the Geneticist to have to collect in order to for her to have five useful batches. Recall that a useful batch means at least two mutations within the three DNA strands.
Explanation / Answer
POSSION DISTRIBUTION
pmf of P.D is = f ( k ) = e- x / x!
where
= parameter of the distribution.
x = is the number of independent trials
I.
mean =
= 1
a.
P( X < 2) = P(X=1) + P(X=0)
= e^-1 * 0 ^ 1 / 1! + e^-1 * ^ 0 / 0!
= 0.73576,
P( X > = 2 ) = 1 - P (X < 2) = 0.26424
b.
P( atmost one of them ) = P( X < = 1) = P(X=1) + P(X=0)
= e^-4 * 4 ^ 1 / 1! + e^-4 * 0 ^ 0 / 0!
= 0.09158
number of mutations per strand of DNA for a simple organism has a Poisson distribution with a mean of 1.
since decides to collect 4 batches an dthe mean rae for 4 stand is = 4
and we also have acriteria that for every 3 at least 2 mutations is collected DNA strands
batches (of three DNA strands) do we expect the Geneticist to have to collect in order to be useful = 4 * 2 / 3 = 2.66