秋 实验6蒙特卡洛模拟Monto Carlo Simulation

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1． Using Monte Carlo simulation, write a Matlab program to calculate an

approximation to  by considering the number of random points lected

inside the quarter circle

Q:xy1,x0,y0

22

where the quarter circle is taken to be inside the square

S:0x1,0y1

解：

counter=0;

N=100000;

for i=1:N

x=rand(1,1);

y=rand(1,1);

if x^2+y^2<1

counter=counter+1;

简介英语 end

end

p=4*counter/N

结果：p = 3.1448

2. Using Monte Carlo simulation, write a Matlab program to calculate

the volume of an ellipsoid（椭球体）

xyz

222

16

248

解：

counter=0;

N=1000;

for i=0:N

x=-4*sqrt(2)+8*sqrt(2)*rand(1,1);

y=-8+16*rand(1,1);

z=清彻 -8*sqrt(2)+16*sqrt(2)*rand(1,1);

if x^2/2+y^2/4+z^2/8<16

counter=counter+1;

end

end

v=counter/N*8*sqrt(2)*16*16*sqrt(2)

结果：v = 2.2528e+003

3. U Monte Carlo simulation to simulate the roll粽子的寓意 s of an unfair

die. Assume the die is biad according to the following

empirical distribution:

Roll Probabil

Value i过分 ty

1河北开学 0.1

2 0.1

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3 0.2

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4 0.3

5 0.2

6 0.1

解：

%v的值代表骰子面的编号

d=rand(1,1);

if d>=0&d<0.1

v=1

elif d>=0.1&d<0.2

v=2

elif d>=0.2&d<0.4

v=3

elif d>=0.4&d<0.7

v=4

elif d>=0.7&d<0.9

v=5

el

d=6

end

4. You arrive at the beach for a ven-day vacation and are dismayed

to learn that the local weather prediction is predicting a 50%

chance of rain every day. Using Monte Carlo simulation, predict

the chance that it rains at least three concutive（接连不断

的，连续而来的） days in your vacation.

解：

counter=0;

N=1e6;

for i=1:N

t=0;

p=rand(1,7);

for j=1:5

if p(j)>=0.5&p(j+1)>=0.5&p(j+2)国庆促销 >=0.5

t=1;

end

end

if t==1

counter=counter+1;

end

end

chance=counter/N

结果：chance =0.3676

5. (Optional) Using Monte Carlo simulation, write a Matlab program

to calculate the volume trapped between the two paraboloids（抛

物体）

z8xyandzx3y

2222

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Note that the two paraboloids interct (相交)on the elliptic

cylinder

x2y4

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解：

x=-10:0.1:10;

y=x;

[X,Y]=meshgrid(x,y);

Z=8-X.^2-Y.^2;

mesh(X,Y,Z)

hold on

马笕菜

z=X.^2+3*Y.^2;

mesh(X,Y,z)

ezplot('X.^2+2*Y.^2-4')

hold off

counter=0;

N=10000;

for i=1:N

x=-2+4*rand(1,1);

y=-sqrt(2)+2*sqrt(2)*rand(1,1);

z=-8+16*rand(1,1);

if x^2+2*y^2<4&z>8-x^2-y^2&z

counter=counter+1;

end

end

counter

v收到的玫瑰花束怎么养 ol=counter/N鱼腥草功效 *4*2*sqrt(2)*16

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X+2 Y-4 = 0

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400

300

200

100

0

-100

-200

10

510

0

-5

Y

-10

-10

-5

X

5

0

实验总结：本次实验主要学习了如何使用Matlab工具进行蒙特卡洛模拟，怀化学院 求出了某些曲边

梯形的面积，并利用蒙特卡罗方法求解了一些概率问题。通过本次实验了解到了蒙特卡罗方

法的应用及其原理。

. .

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