# Thread: maximum value of poisson variable

1. ## maximum value of poisson variable

1. When 10 people buy 1,000 lottery for each person, with the probability of winning 0.001.
Find out the probability distribution of the maximum number of winning per one person.
Which value takes the maximum probability?

2. When 100 people buy 1,000 lottery for each person, with probability of winning 0.001.
Find out the probability distribution of the maximum number of winning per one person.
Which value takes the maximum probability?

I know that lottery problem is directly related to Possion distribution, but I do not know how to deal with "maximum nuber of winning per person". Help me!

2. Originally Posted by kb8319
1. When 10 people buy 1,000 lottery for each person, with the probability of winning 0.001.
Find out the probability distribution of the maximum number of winning per one person.
Which value takes the maximum probability?

2. When 100 people buy 1,000 lottery for each person, with probability of winning 0.001.
Find out the probability distribution of the maximum number of winning per one person.
Which value takes the maximum probability?

I know that lottery problem is directly related to Possion distribution, but I do not know how to deal with "maximum nuber of winning per person". Help me!
Let the probability of a player winning $\displaystyle $$n times on \displaystyle$$N$ tickets be $\displaystyle p(n,N)$. Then the probability that of $\displaystyle $$k players each buying \displaystyle$$N$ tickets the largest number of winning tickets held by a player is $\displaystyle $$n is: \displaystyle p_{max}(n,k,N)=k\, p(n,N)\, [p(<n,N)]^{k-1} where \displaystyle p(<n,N) is the probability of a single player winning on less than \displaystyle$$n$ times from $\displaystyle$$N$ tickets.

CB