easy Probability

Uniform Fix

A release-checked easy problem for training Conditional Expectation, Expected Value, Continuous Random Variables.

Question

Let $U \sim \text{Unif}(0,1)$ and $X_1,X_2,\dots \sim \text{Unif}(0,1)$ IID. Define $N = \text{min}\{n \in \mathbb{N} : X_n > U\}$. Find $\mathbb{E}[N]$. Enter $-1$ if the answer is infinite.

Practice focus

This Probability problem is tagged Conditional Expectation, Expected Value, Continuous Random Variables. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.