Hands-On Mathematics for Deep Learning

Sampling with or without replacement

Let's now assume that there is a total of n items in the bucket and we must pick r of them. Then, let R = {1, 2,…, r} be the list of items picked and let N = {1, 2, …, n} be the total number of items. This can be written as a function, as follows:

Here, f(i) is the i^th item.

Sampling with replacement is when we pick an item at random and then put it back so that the item can be picked again.

However, sampling without replacement refers to when we choose an item and don't put it back, so we cannot pick it again. Let's see an example of both.

Say we need to open the door to our office and we have a bag containing ...