Continuous Probability Densities — Grinstead & Snell
Mathematics — Probability · discrete-probability-geometric
Problem
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 ∑ωm(ω)=1.