Question

Use R code to answer question. There is 2 parts to the question, the first being straight forward and the second using a monte carlo method.

Question:

Let U and V both follow Uniform(0,1) distributions. Find two methods to simulate the

distribution of U+V. The first method should directly simulate the distribution using

uniforms, and the second should use a Monte Carlo method.

Hint:

--First: call two random uniforms and add. Second:

--Generate uniform between 0 and 2 (x), then

another between 0 and ½ (y). Sum of two uniforms is a

line straight up to ½ (occurring at x=1)

then down to 0 (occurring at x=2). Accept randomly generate point if either is true: For x < .5, y < x/2. For x > .5, y < .5 – x/2. Otherwise, reject point.

I think the first part is just something like x = runif(1) + runif(1). I have no idea how to complete the 2nd part using monte carlo.

Answer 1