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P(k|n,s) , what type of probability is this?

I have to do a seminar and it has some maths in it, which i can't grasp.

I know about probability of one variable, two variables and prob of one variable given the other variable.

https://fc33baf3-a-62cb3a1a-s-sites....attredirects=1

NOTE( i have uploaded the file as attachment)

please check page 2 of this pdf. you will see an equation **n=arg max P(k|n,s)**

How should i read this equation.?what does it mean mathematically? Can u provide some references?

I also don't have any idea about the Theorem 1 given

*"Theorem 1: If k < n, ^n is unique and is the smallest integer*

*j k, which satisfies j+1......" *

Please go through the page and give me some idea.

Re: P(k|n,s) , what type of probability is this?

Hey lavacelava.

Basically it means that you find the specific n that gives the maximum probability (for all values of n) and you return that specific value of n.