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## Homework Statement

A die is rolled until the first time that a six turns up. We shall see that the

probability that this occurs on the nth roll is (5/6)n−1 · (1/6). Using this fact,

describe the appropriate infinite sample space and distribution function for

the experiment of rolling a die until a six turns up for the first time. Verify

that for your distribution function the Ʃ(ω)=1, as ω→∞

## Homework Equations

Relevant equations are in the question.

## The Attempt at a Solution

Ω = { 6, N6, NN6, NNN6, ... , N...N6 }

Also, I know that the equation is exponential decay, but I just don't know how to get the formula...

I also know that it adds up, because (1/6)+(5/6)(1/6) + (5/6)^2(1/6) .. etc eventually equal to 1 as N→∞

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