Misspelled words in a document n is the number of

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: on with parameters k and p. More generally, for 0 ≤ k < l, the increment Cl − Ck is the number of ones in k − l Bernoulli trials, so it has the binomial distribution with parameters l − k and p. Also, the increments of C over nonoverlapping intervals are independent. • The cumulative numbers of trials for j ones, for j ≥ 0: (S0 , S1 , S2 , . . .). As discussed below, for integers r ≥ 1, Sr has the negative binomial distribution with parameters r and p. Negative binomial distribution In the remainder of this section we discuss the distribution of Sr , which is the number of trials required for r ones, for r ≥ 1. The possible values of Sr are r, r + 1, r + 2, . . . . So let n ≥ r, and let k = n − r. The event {Sr = n} is determined by the outcomes of the first n trials. The event is true if and only if there are r − 1 ones and k zeros in the first −1 k + r − 1 trials, and trial n is a one. There are n−1 such sequences of length n, and each has r probability pr (1 − p)...
View Full Document

Ask a homework question - tutors are online