R comes with a set of pseuodo-random number generators that allow you to simulate from well-known probability distributions like the Normal, Poisson, and binomial. Explain the differences by among following functions by defining what they do mathematically and then by using an example:

1. rnorm
2. dnorm
3. pnorm
4. rpois

Simulate 100 standard Normal random numbers and then show them in the histogram:

1. Normal random numbers with mean 0 and standard deviation 1.
2. Normal random numbers with mean 20 and standard deviation 2

Create and then explain the output of the following:

1. Draw randomly 10 numbers from a uniform distribution of numbers from 100 to 10,000.
2. Do a random permutation from a sample of numbers from 1 to 200 that are uniformly distributed.
3. Create a sample w/replacement for numbers from 10 to 100 that are uniformly distributed.