Topic : Probability/Expected value/Geometric Distribution
Short Discription :
Given a dice with n sides, you have to find the expected
number of times you have to throw that dice to see all its faces at least once.
Assume that the dice is fair, that means when you throw the dice, the
probability of occurring any face is equal.
Idea:
First of all, the probability of coming the first unexposed
face of the dice is 
, as still no face has come up before it.
Than the probability of coming the second unexposed face of
the dice is 
, as one face has come up already.
Similarly, the probability of coming the ith unexposed face of the dice is}{n} "p_i = \frac{n-(i-1)}{n}")
Similarly, the probability of coming the ith unexposed face of the dice is
This is clearly a geometric distribution.
We know expected value in geometry distribution is , &space;=&space;\frac{1}{p} "E(x) = \frac{1}{p}")
so, our expected result
so, our expected result
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