View the step-by-step solution to:

Question

Suppose X ∼ Binomial(n, p). This exercise relates the distribution function of the binomial to the beta

distribution. (a) Show that for p ∈ (0, 1), P[U(k+1) > p] = P[X ≤ k]. [Hint: The (k + 1) st order statistic is greater than p if and only if how many of the Ui 's are less than p? What is that probability?] (b) Conclude that if F is the distribution function of X, then F(k) = P[Beta(k + 1, n − k) > p]. This formula is used in the R function pbinom.

Top Answer

The first part is straightforward. The second part can be solved using the following formula, if U 1... View the full answer

Sign up to view the full answer

Why Join Course Hero?

Course Hero has all the homework and study help you need to succeed! We’ve got course-specific notes, study guides, and practice tests along with expert tutors.

  • -

    Study Documents

    Find the best study resources around, tagged to your specific courses. Share your own to gain free Course Hero access.

    Browse Documents
  • -

    Question & Answers

    Get one-on-one homework help from our expert tutors—available online 24/7. Ask your own questions or browse existing Q&A threads. Satisfaction guaranteed!

    Ask a Question