《随机过程》课程实验报告.docx

《随机过程》课程实验报告.docx

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《随机过程》课程实验报告

一、实验问题

1.编制程序产生并输出100个二项分布的随机数，

.

2.进行三次Poisson过程的模拟，

作图：

（在同一直角坐标系下，作出‘

’的关系图

二、问题的分析

Ⅰ随机数的产生：

⑴

分布随机数的产生。

⑵非

分布随机数的产生。

Ⅱ⑴

为连续的随机变量，分布函数为

①

②设

的密度函数为

则有

⑵离散分布随机数的产生

的分布列为

…

…

则有

服从上述分布列.

⒈先求出

的分布列，再由上述Ⅱ

（2）的方法计算.

⒉由Ⅱ

（1）算出

.

三、程序设计

1.

%该函数用于输出服从所给定的X~b（k,p1）的m个随机数

%e，E分别为所输出随机数的和原先的均值

%v，V分别为所输出随机数的和原先的方差

%p值为给定的X~b（k,p1）的分布列中的概率

functionr=bino（m,n,k,p1）

g=0:

n;

y=binocdf（g,k,p1）

fori=2:

（k+1）

p

（1）=y

（1）;

p（i）=y（i）-y（i-1）;

end

R=rand（1,m）

forj=1:

m

forl=2:

k

if0

（1）

x（j）=0;

elseify（l-1）

x（j）=l-1;

end

end

end

end

p

x

e=mean（x）

E=k*p1

v=var（x）

V=k*p1*（1-p1）

end

2.

%该程序用于输出Poisson过程的模拟

%m1，m2，m3为Poisson过程的最终人数，n为Poisson过程的强度

%x,y,z分别m1，m2，m3个人所到达的的时间间隔

%t1,t2,t3分别m1，m2，m3个人所到达的的时刻

%k1,k2,k3检验是否与Poisson过程的强度相近

functiong=poisson1（m1,m2,m3,n）

R1=rand（1,m1）;

R2=rand（1,m2）;

R3=rand（1,m3）;

fori=1:

m1

x（i）=-（log（1-R1（i）））/n;

end

x

fori=1:

m2

y（i）=-（log（1-R2（i）））/n;

end

y

fori=1:

m3

z（i）=-（log（1-R3（i）））/n;

end

z

fori=2:

m1

t1

（1）=x

（1）;

t1（i）=t1（i-1）+x（i）;

end

fori=2:

m2

t2

（1）=y

（1）;

t2（i）=t2（i-1）+y（i）;

end

fori=2:

m3

t3

（1）=z

（1）;

t3（i）=t3（i-1）+z（i）;

end

t1

t2

t3

k1=m1/t1（m1）

k2=m2/t2（m2）

k3=m3/t3（m3）

N1=1:

m1;

N2=1:

m2;

N3=1:

m3;

plot（t1,N1,'g.'）

holdon

plot（t2,N2,'r.'）

holdon

plot（t3,N3,'.'）

gridon

xlabel（'t'）

ylabel（'N'）

title（'Poisson¹ý³ÌÄ£Äâ'）

3.

%该程序用于markov链模拟

%R服从U~（0,1）,s=[0123]

%p为转移概率矩阵A各行的概率累积值，X0,X1,X2,X3分别为从状态空间里的0,1,2,3为初值

functionr=markov（A,k）

x=[0123];

n=length（A）;

R=rand（1,k）;

g1=1;

g2=2;

g3=3;

g4=4;

fori=0:

（n-1）

forj=2:

n

p（i+1,1）=A（i+1,1）;

p（i+1,j）=A（i+1,j）+p（i+1,j-1）;

end

end

form=1:

k

forj=2:

n

if0

X0（m）=x

（1）;

elseifp（g1,j-1）

X0（m）=x（j）;

end

end

end

g1=X0（m）+1;

end

form=1:

k

forj=2:

n

if0

X1（m）=x

（1）;

elseifp（g2,j-1）

X1（m）=x（j）;

end

end

end

g2=X1（m）+1;

end

form=1:

k

forj=2:

n

if0

X2（m）=x

（1）;

elseifp（g3,j-1）

X2（m）=x（j）;

end

end

end

g3=X2（m）+1;

end

form=1:

k

forj=2:

n

if0

X3（m）=x

（1）;

elseifp（g4,j-1）

X3（m）=x（j）;

end

end

end

g4=X3（m）+1;

end

p

R

X=[0X0]

Y=[1X1]

Z=[2X2]

F=[3X3]

N=0:

100;

plot（N,X,'r-'）

holdon

plot（N,Y,'m*'）

holdon

plot（N,Z,'g+'）

holdon

plot（N,F,'b-.'）

xlabel（'X'）

ylabel（'N'）

title（'markov链模拟，状态空间s=[0123]'）

四、问题求解结果与结论

1.

bino（100,10,10,0.6）

y=

0.00010.00170.01230.05480.16620.36690.61770.83270.95360.99401.0000

R=

Columns1through11

0.10480.85840.69820.73370.65050.51630.32640.66180.11760.14780.0198

Columns12through22

0.96430.97040.12390.46740.65670.29020.75450.55810.42780.26720.7537

Columns23through33

0.89840.72840.40680.93830.25540.53320.95480.26770.25010.92770.0686

Columns34through44

0.29940.59160.20330.63590.79840.50170.65080.79600.23340.60080.1125

Columns45through55

0.51580.83780.92080.49820.27760.65250.91730.50980.97420.19730.1112

Columns56through66

0.29740.39640.42080.31150.69380.09190.40210.29520.30650.10560.5938

Columns67through77

0.28270.15520.00070.28360.55080.87090.04230.90470.13100.83370.8005

Columns78through88

0.91790.13730.50470.40500.17360.57520.60620.21440.51990.98920.4899

Columns89through99

0.69490.41140.03480.29280.80140.34650.08330.51110.36680.73950.5247

Column100

0.8045

p=

0.00010.00160.01060.04250.11150.20070.25080.21500.12090.04030.0060

x=

Columns1through19

4877765744399467576

Columns20through38

6578768569558456577

Columns39through57

6775646886578695456

Columns58through76

6574655465415683848

Columns77through95

7846656656967635754

Columns96through100

65767

e=

5.9400

E=

6

v=

2.3600

V=

2.4000

2.poisson1（50,100,200,3）

x=

Columns1through12

0.86591.00610.02300.97380.22880.02350.05560.11700.06160.44290.70590.6356

Columns13through24

0.37160.53400.03530.24650.02020.56000.14140.58850.43030.13710.07920.1384

Columns25through36

0.20500.25080.17090.46470.00910.15650.06890.15510.13390.00620.38530.3719

Columns37through48

0.59670.19110.33660.36470.14660.12780.39020.00890.93740.32830.04840.9296

Columns49through50

0.21030.9020

y=

Columns1through12

1.20700.11150.25800.00420.05700.14440.49450.12870.26880.15940.46241.4015

Columns13through24

0.19750.02590.03530.13660.11520.82950.23420.28860.01770.10340.50910.2574

Columns25through36

0.93650.25710.17751.10890.30470.94490.47710.03920.11190.07970.17860.2322

Columns37through48

0.61340.50410.29210.24400.11850.39060.32950.49930.67500.00890.31860.0737

Columns49through60

0.66690.87800.62630.01320.24970.15080.02420.09510.02030.08770.91340.5479

Columns61through72

0.01291.14890.88660.01570.13330.42020.01070.09270.12200.59860.24590.0409

Columns73through84

0.05000.17280.05780.96350.04640.08620.00900.73820.42540.07610.13880.3024

Columns85through96

0.31600.02270.06480.06350.64710.28880.07510.37510.03490.00140.27500.1469

Columns97through100

0.18850.10680.23490.1017

z=

Columns1through12

0.00190.86350.22740.08330.72110.04270.25310.06221.12310.96760.22550.0610

Columns13through24

0.41360.47130.21790.60370.60480.28160.50940.21530.50120.75441.04440.0469

Columns25through36

0.32820.46150.07060.19550.11510.19090.37980.09720.68560.25610.81160.2091

Columns37through48

0.15570.39420.47150.79700.02140.51000.06130.59630.04620.22580.60960.2880

Columns49through60

0.10750.15000.25480.92800.11100.34040.01280.47180.06920.23750.29890.0911

Columns61through72

0.22170.84450.15010.02190.31090.06380.33260.14710.39150.01890.13190.3163

Columns73through84

1.35470.20210.09740.01260.27730.01560.92570.20170.67920.87260.38140.1473

Columns85through96

0.53920.28620.38010.29110.79920.76210.20310.06700.13240.00800.00240.5424

Columns97through108

0.09260.52430.53480.07650.22560.63250.32750.08061.20120.25660.59990.5635

Columns109through120

0.26980.18650.11520.54091.49620.23670.07060.25970.09530.16560.07710.5136

Columns121through132

0.21360.21350.42220.04571.00400.44250.32130.27490.08620.72110.24050.1808

Columns133through144

0.49770.39821.54440.29960.05670.04670.06230.02280.15680.43200.16430.0122

Columns145through156

0.00190.35590.46570.02330.13810.22930.12460.37160.55080.37660.88990.3395

Columns157through168

0.28361.55840.01870.02961.08350.17330.38540.17361.76550.60650.09410.1796

Columns169through180

0.15400.52310.01090.53070.01150.00620.19770.60570.52990.92080.07490.6618

Columns181through192

0.09850.02051.15450.02260.08690.01120.04560.37980.00960.63660.11050.1827

Columns193through200

0.35310.84860.11531.13510.50380.03010.06570.0704

t1=

Columns1through12

0.86591.87201.89502.86883.09763.12113.17673.29373.35533.79824.50415.1397

Columns13through24

5.51136.04536.08066.32716.34736.90737.04877.63728.06758.20478.28388.4223

Columns25through36

8.62728.87809.04909.51369.52279.67929.74819.903210.037110.043310.428610.8005

Columns37through48

11.397211.588311.924912.289612.436212.564012.954212.963013.900414.228714.277115.2068

Columns49through50

15.417016.3191

t2=

Columns1through12

1.20701.31861.57651.58081.63771.78222.27662.40532.67412.83353.29584.6974

Columns13through24

4.89494.92084.95605.09275.20796.03746.27166.56026.57796.68137.19047.4478

Columns25through36

8.38438.64148.81909.927910.232611.177511.654611.693811.805611.885312.063912.2961

Columns37through48

12.909413.413613.705613.949614.068014.458614.788115.287515.962415.971416.290016.3636

Columns49through60

17.030617.908518.534818.548018.797718.948518.972719.067919.088219.175920.089220.6371

Columns61through72

20.650021.798922.685522.701222.834523.254723.265323.358123.480124.078724.324624.3655

Columns73through84

24.415524.588324.646225.609725.656025.742225.751226.489426.914826.990827.129627.4320

Columns85through96

27.748027.770727.835427.898928.546028.834828.910029.285029.320029.321329.596329.7432

Columns97through100

29.931830.038530.273530.3752

t3=

Columns1through12

0.00190.86541.09281.17611.89721.93992.19302.25523.37844.34594.57154.6325

Columns13through24

5.04615.51745.73536.33896.94387.22537.73487.95008.45129.205710.250010.2970

Columns25through36

10.625211.086711.157311.352811.467911.658812.038612.135812.821413.077513.889214.0982

Columns37through48

14.253914.648115.119515.916515.937916.447916.509217.105517.151717.377517.987018.2750

Columns49through60

18.382518.532518.787319.715319.826320.166720.179520.651320.720520.958021.256921.3480

Columns61through72

21.569722.414222.564322.586222.897122.960823.293423.440523.832023.850923.982924.2991

Columns73through84

25.653925.856025.953425.966026.243326.258927.184627.386328.065528.938129.319529.4668

Columns85through96

30.006130.292330.672430.963531.762732.524832.727932.795032.927432.935432.937833.4802

Columns97through108

33.572834.