(Solved): 1. Design a rejection sampling algorithm for generating samples from a distribution with the follo ...

1. Design a rejection sampling algorithm for generating samples from a distribution with the following pdf: $$?(x)=x^3+\frac{5}{4}{x}^2+\frac{1}{3}x+\frac{1}{6},0?x?1.$$ Describe your rejection sampling algorithm. Implement your algorithm to generate 1000 (accepted) samples from this distribution. Based on the 1000 samples you generated, give an estimate of $$E\left(X^2\right)$$, where $$X$$ follows distribution $$?(x)$$, and the standard error of your estimate. Attach your code and results.