Cutting random pieces of string

Probability Level 3

From a string of length 1 m,1 \text{ m}, we choose a length uniformly at random between 0 m0 \text{ m} and 1 m,1 \text{ m}, and cut as many of these lengths as possible from the string.

What is the expected length of the remaining string (in meters)?


Bonus: If we have a random number aa chosen with uniform distribution over the interval (0,1n],\big(0,\frac{1}{n}\big], where nNn\in\mathbb{N}, what's the expected value of the remainder 1moda1\bmod a for a particular n?n?

×

Problem Loading...

Note Loading...

Set Loading...