MATLAB实验报告6.docVIP

Using Monte Carlo simulation, write a Matlab program to calculate an approximation to ( by considering the number of random points selected inside the quarter circle where the quarter circle is taken to be inside the square count=0; n=10000; for i=1:n x(i)=rand(1); y(i)=sqrt(1-(x(i))^2); z=rand(1); if z=y(i) count=count+1; end; end; s=count/n PI=4*s 结果：s =0.7869 PI =3.1476 s =0.7819 PI =3.1276 s =0.7828 PI =3.1312 Using Monte Carlo simulation, write a Matlab program to calculate the volume of an ellipsoid（椭球体） count=0; n=10000; for i=1:n x(i)=sqrt(32)*rand(1); y(i)=8*rand(1); z(i)=sqrt(8*16-4*(x(i))^2-2*(y(i))^2); u=sqrt(128)*rand(1); if u=z(i) count=count+1; end; end; v=4*count/n*sqrt(32*64*128) 结果： v = 1.0758e+003 v = 1.0627e+003 v = 1.0818e+003 3、Use Monte Carlo simulation to simulate the rolls of an unfair die. Assume the die is biased according to the following empirical distribution: Roll Value Probability 1 0.1 2 0.1 3 0.2 4 0.3 5 0.2 6 0.1 设pi（i=1，2，3，4，5，6）表示色子显示i点的概率。 count=[0 0 0 0 0 0]; n=12000; for i=1:n x(i)=rand(1); if x(i)=0.1 count(1)=count(1)+1; elseif x(i)0.1 x(i)=0.2 count(2)=count(2)+1; elseif x(i)0.2 x(i)=0.4 count(3)=count(3)+1; elseif x(i)0.4 x(i)=0.7 count(4)=count(4)+1; elseif x(i)0.7 x(i)=0.9 count(5)=count(5)+1; else count(6)=count(6)+1; end; end; for k=1:6 p(k)=count(k)/n; end for i=1:6 fprintf(p%d:%f ,i,p(i)); end 结果： p1:0.105083 p2:0.097583 p3:0.202917 p4:0.294667 p5:0.203333 p6:0.096417 p1:0.095750 p2:0.098667 p3:0.208333 p4:0.297000 p5:0.201250 p6:0.099000 p1:0.098417 p2:0.100000 p3:0.198417 p4:0.299917 p5:0.194250 p6:0.109000 4.You arrive at the beach for a seven-day vacation and are dismayed to learn that the local weather prediction is predicting a 50% chance