Geometric and negative binomial distributions
Probability theory · Mathematics
Study notes
Q: A die is rolled until the first 6. Find P(first 6 on 3rd roll) and the expected rolls. p = 1/6. P(X=3) = (5/6)^2 (1/6) = 25/216 = 0.1157. E(X) = 1/p = 6 rolls expected. Negative binomial: P(3rd six on 10th roll) = C(9,2)(1/6)^3(5/6)^7.