Suppose that X has the binomial distribution with parameters n and p, and that Y has the negative binomial distribution with parameters r and p, where r is a positive integer Show that Pr(X r) Pr(Y n r) by showing that both the left side and the right side of this equation can be regarded as the pr...

Consider the event that less than r successes are obtained in the first n Bernoulli trials The ...

Suppose that X has the binomial distribution with parameters n and p, and that Y has the

Question:

Suppose that X has the binomial with parameters n and p, and that Y has the negative binomial with parameters r and p, where r is a positive integer. Show that Pr(X < r) = Pr(Y > n − r) by showing that both the left side and the right side of this equation can be regarded as the probability of the same event in a sequence of Bernoulli trials with probability p of success.
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...