Carry out the Monte Carlo approximation in Computer Problem 9.1.3 with quasi-random numbers from the Halton sequence for , and 5. For part (c), use and for the x and y coordinates, respectively. Code needs to be in MatLab.Problem 9.1.3 is: a. Using calculus, find the area bounded by the two parabolas P1?(x)=x2?x+1/2andP2?(x)=?x2+x+1/2. b. E solutionspile.com

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Carry out the Monte Carlo approximation in Computer Problem 9.1.3 with quasi-random numbers from the Halton sequence for , and 5. For part (c), use and for the x and y coordinates, respectively. Code needs to be in MatLab.

Problem 9.1.3 is:

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a. Using calculus, find the area bounded by the two parabolas

P_{1} (x) = x^{2} ? x + 1/2 and P_{2} (x) = ? x^{2} + x + 1/2 .

b. Estimate the area as a Type 1 Monte Carlo simulation, by finding the average value of

P_{2} (x) ? P_{1} (x)

on

[0, 1]

. Find estimates for

n = 1 0^{i}

for

2 ? i ? 6

. c. Same as (b), but estimate as a Type 2 Monte Carlo problem: Find the proportion of points in the square

[0, 1] \times [0, 1]

that lie between the parabolas.

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