Question

Use simulations to prove that the binomial distribution is correct. The binomial distribution has two parameters n and p. There are n trials and each has two possible outcomes, with probability p for “success” and 1-p for “failure”. The binomial gives the probability distribution for the number of successes in n trials. You will conduct simulations with r replicates, where each simulation replicates does n simulated “coin flips”. You will add up the number of successes in each coin flip, and compare the result to the true distribution:

1. Generate n*r values from the uniform(0,1) distribution and arrange these in an nxr matrix. Each value less than p is considered a “success”.

ii. For each row from part I, count the number of successes. The number of possible successes ranges from 0 to n.

iii. Use the table function to count up the number of replicates with each number of successes.

iv. Make a table that compares the simulation result to the true binomial probabilities.

DO NOT USE LOOPS AND DO IT VECTORIZED AS MUCH AS POSSIBLE.

(DO IN R OR PYTHON)

Answer 1