### Problem 2

How many time do we need to toss to estimate the fairness of a coin?

Checking whether a coin is fair

### Problem 1

The expectation times of sampling to get a number twice from a discrete uniform distribution .

denotes the probability that are distinct numbers, and .

### Solution

**Expectation**:

where

**Variance**:

I donâ€™t find a good way to calculate it yet.

### Problem 0

Sample numbers without replacement from . Let . Find and .

### Solution