Introduction to Probability · Problem 4.3.5

Distributions and Densities — Grinstead & Snell

Mathematics — Probability · conditional-probability-paradoxes

Problem

Using the notation introduced in Example 4.29, let

p_x = \begin{cases} \frac{2}{3}\left(\frac{1}{3}\right)^k, & \text{if } x = 2^k, \\ 0, & \text{otherwise.} \end{cases}

Show that there is exactly one value of

x

such that if your envelope contains

x

, then you should switch.