Using R or python if needed:

Assume you would like to generate a Beta(4, 3) distribution using the acceptance-rejection.

Recall that the pdf of a Beta(, ) distribution is: f(x|, ) = [x¹(1 x)¹]/B(, ) , x [0, 1] where B(, ) is the "Beta function". In R, this function is called beta. Assume that you can generate numbers from a uniform distribution on (0, 1). Please do the following:

Write the pdf for the Beta(4, 3) distribution after finding the value in the denominator of the pdf, B(4, 3).

Determine the x value for which the Beta(4,3) pdf takes it's maximum value. (You will need to differentiate the pdf by hand)

Using the information from the last part, determine the acceptance-rejection rule that you could use to generate a Beta(4, 3) distribution from Unif(0, 1)

Using the last part, generate 10,000 values from a Beta(4, 3) distribution. Make a histogram and compare to the theoretical distribution given by the pdf of the Beta(4, 3) distribution.