Four ways to pick a sample

You will write three functions that choose a sample in the ways of this lesson: a systematic sample, the places of a stratified sample, and a cluster sample.

The idea. A systematic sample takes every $k$th item after a start. Proportional allocation gives a stratum of size $N_i$ the share $n \times \dfrac{N_i}{N}$ of the places. A cluster sample chooses whole groups at random and keeps every member of them.

Your tasks.

1. Finish systematic(frame, k, start). Return the items at positions start, start + k, start + 2k and so on. Positions count from 0, as in a Python list.
2. Finish allocate(sizes, n). Return a list with the number of places for each stratum, rounded to whole numbers.
3. Finish cluster(clusters, how_many). Choose how_many clusters with random.sample and return one list of all their members.