DATA 605 FUNDAMENTALS OF COMPUTATIONAL MATHEMATICS

7 A die is rolled until the first time T that a six turns up.

1. What is the probability distribution for T?

\(P(T = t) = 1/6 * 5/6^{t-1}\)

2. Find P(T > 3).

p <- 1/6
k <- 2
(T3 <- pgeom(k, p, lower.tail = F))

## [1] 0.5787037

3. Find P(T > 6|T > 3).

p <- 1/6
k <- 5
T6 <- pgeom(k, p, lower.tail = F)

T3 * T6 / T3

## [1] 0.334898