Use Excel to produce a Monte Carlo approximation of the beta distribution

The beta distribution is a family of continuous probability distributions defined on the interval of (0,1) in terms of two positive parameters, denoted as alpha and beta, that appear as exponents of the variable and its complement to 1 respectively and control the distribution.

The beta distribution in its present form was first introduced by the British mathematician and statistician Karl Pearson in 1901. It is a continuous probability distribution often used to model the uncertainty about the probability of success of an experiment.

The beta distribution can be used to analyse probabilistic experiments, called Bernoulli experiments, that have only two possible outcomes, being:-

1. Success, with probability X
2. Failure, with probability 1-X

Beta distributions occur less frequently in nature than other distributions like normal and exponential, but they are still quite useful in various contexts, particularly for modelling probabilities and proportions.

Some situations where beta distributions can be applied are:-

1. Beta distributions are widely used in Bayesian statistics to model prior distributions of probabilities.
2. Beta distributions are used to…