Thank you for looking at my question. I am trying to solve this homework question.
Consider the problem of sequencing genome by random reads. If G is the length of the entire sequence, L is the length of the read and n is the number of reads, then coverage is defined as nL/G. Now, if we want 50% of the original long sequence to be covered by at least one fragment, how much coverage do we need?
I read Lander-Waterman http://www.genetics.wustl.edu/bio5488/lecture_notes_2005/Lander.htm model to understand the concept. But didn't quite get how to solve this problem. I thought to consider the given 50% as probability and y as 1 (the one from Poisson distribution) and calculate lambda (that is the coverage). But I don't think I am on right track. I thought of considering y as 1 because the question says 50% of the original long sequence to be covered by atleast one fragment, which means that those bases are sequenced atleast once.
I may be wrong.
Experts can you guide me please.
Thank you.
I think you're not off so far. As I read it y=1 means that the bases are read "exactly once" and not "at least once". You would need to calculate the coverage under the probability of 0.5 for P(y=1) + P(y=2) + ... which is equal to ...