## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

No credit card required

Problem 14

Bayes, Laplace, and Philosophies of Probability (1764, 1774)

Problem. Assume that the probability p of an event A is equally likely to be any number between 0 and 1. Show that, conditional on A having previously occurred in a out of n independent and identical trials, the probability that p lies between p1 and p2 is Solution. Let Xn be the number of times that the event A occurs in n trials. Since p is equally likely to be between 0 and 1, we let p have a probability density function that is uniform on [0,1], that is, To find , let us first obtain the conditional density by using Bayes' Theorem1: Now, we have2 Therefore, Hence, as required.

# 14.1 Discussion

This is essentially ...

## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

No credit card required