If a gene is expressed at a level of 1/1200 compared to the average gene, how is probability 50:50 that we have a read mapped to it?
I actually disagree with that.. I guess I write this down as a discussion.
The expected value for an average gene is 1200. For this gene at 1/1200 expression, you expect 1 read.
However, because of sampling, sometimes you get 0, 1 or 2. If we assume the sampling follows a poisson distribution, we can calculate the probability of getting 0, 1 , 2 ... reads:
plot(dpois(0:10,lambda=1),ylab=&quot;Probability&quot;,xlab=&quot;No of reads&quot;)


The probabilities are like:
data.frame(n=0:5,p=dpois(0:5,lambda=1))

  n           p
1 0 0.367879441
2 1 0.367879441
3 2 0.183939721
4 3 0.061313240
5 4 0.015328310
6 5 0.003065662

The probability of getting exactly 0 or 1 read should be ~0.37. The probability of getting at least 1 read would be 1 - P(n=0) = 1- 0.367879441 = 0.6321206