Simulating a random variable

You will find the expected value and the variance of a table, then simulate many days and check that the simulation settles at the expected value and the standard deviation. The checker uses the made-up delivery van.

The idea. $E(X) = \sum x\,p$ and $\sigma^2 = \sum (x - \mu)^2 p$. A simulation draws values with rng.choices(values, weights=probs, k=days), where rng is a random generator with a fixed seed. Its mean and standard deviation should come close to $\mu$ and $\sigma$.

Your tasks.

1. Finish expected(pmf).
2. Finish variance(pmf). Use expected(pmf) for the mean.
3. Finish simulate(pmf, days, seed). Make rng = random.Random(seed) and return the list of simulated values.