概率論第二次試驗

1、概率論第二次試驗報告 姓 名 楊帆學 號：4012014057姓 名 楊藍學 號：4012014025姓 名 張藝朋學 號：4012014047123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899010203040506070809101112131415161718192

2、021222324252627282930313233343536 #正態(tài)分布#第一問curve(dnorm(x,mean = -2,sd=1,log=FALSE),type = "l",add = TRUE,xlim=c(-5,5),ylim=c(0,1),ylab = "概率")curve(dnorm(x,mean = 0,sd=1,log=FALSE),type = "l",add = TRUE,col="red")curve(dnorm(x,mean = 2,sd=1,log=FALSE),type = &

3、quot;l",add = TRUE,col="green")curve(pnorm(x,mean = -2,sd=1),type = "l",add = TRUE)curve(pnorm(x,mean = 0,sd=1,lower.tail = TRUE,log.p = FALSE),type = "l",add = TRUE,col="red")curve(pnorm(x,mean = 2,sd=1,lower.tail = TRUE,log.p = FALSE),type = "l&quo

4、t;,add = TRUE,col="green")title(main = "正態(tài)分布")mtext("-單調(diào)的是分布函數(shù)", adj = 1,line = -1)mtext("-不單調(diào)的是概率密度", adj = 1, line = -2)text(x=-3,y=0.6,labels="= -2")text(x=-1,y=0.6,labels="= 0",col="red")text(x=1,y=0.6,labels="= -2",

5、col="green")#第二問curve(dnorm(x,mean = 0,sd=0.5,log=FALSE),type = "l",add = TRUE,lwd=4,xlim=c(-5,5),ylim=c(0,1),ylab = "概率")curve(dnorm(x,mean = 0,sd=1,log=FALSE),type = "l",add = TRUE,col="red")curve(dnorm(x,mean = 0,sd=2,log=FALSE),type = "l&quo

6、t;,add = TRUE,col="green")curve(pnorm(x,mean = 0,sd=0.5),type = "l",add = TRUE)curve(pnorm(x,mean = 0,sd=1,lower.tail = TRUE,log.p = FALSE),type = "l",add = TRUE,col="red")curve(pnorm(x,mean = 0,sd=2,lower.tail = TRUE,log.p = FALSE),type = "l",add =

7、TRUE,col="green")title(main = "正態(tài)分布")mtext("-單調(diào)的是分布函數(shù)", adj = 1,line = -1)mtext("-不單調(diào)的是概率密度", adj = 1, line = -2)text(x=-3,y=0.6,labels="= -2")text(x=-1,y=0.6,labels="= 0",col="red")text(x=1,y=0.6,labels="= -2",col="

8、;green")#泊松分布x<-seq(0,30)plot(x,dpois(x,1),type="b")lines(x,dpois(x,2),type="b",col="red")lines(x,dpois(x,3),type="b",col="green")lines(x,dpois(x,6),type="b",col="blue")#二項分布p<-0.2x<-seq(0, n, by = 1)f= choose(10,x)

9、* px * (1-p)(10-x) p= choose(20,x) * px * (1-p)(20-x) g= choose(50,x) * px * (1-p)(50-x) plot(x,g, type = "l", ylab = "p(x)",main = "二項分布概率分布圖")lines(x,p, col = "red", lwd = 2)lines(x,f, col = "green", lwd = 2)mtext("f = choose(n,x) * px * (1-p)

10、(n-x) ", adj = 0)mtext("最大概率", adj = 0, line = -1, font = 4)#二項分布的泊松逼近x <- seq(0, 40, 1)plot(x,dbinom(x, size=40,prob=0.2, log = FALSE), type = "p", ylab = "F(x)", main = "二項分布的泊松逼近")curve(dpois(x,lambda = 8, log = FALSE),type = "p",col="

11、;red",ylim=c(0,1), xlim=c(0,10),add = TRUE)mtext("-二項分布B（k；40,0.2） ", adj = 1,line = -1)mtext("-泊松分布（8） ", adj = 1, line = -2,col="red")#服務窗口問題#m_plot<-array(0,dim = c(1:15)#m_x<-array(0,dim = c(1:15)a<-0b<-0p<-0.1n<-200 #ns<-3 #s為排隊人數(shù)shiyan_nu

12、m<-1000alpha<-0.8 for (m in 1:15) b=0 for (j in 1:shiyan_num) a=0 for (i in 1:n) x=rbinom(1,1,p) if(x=1) a=a+1Z if(a<=m*s) b=b+1 # m_plot1,m<-b/shiyan_num print(b/shiyan_num)#plot(m_x1, ,m_plot1, )#高爾頓釘板實驗n<-5000zhixing<-function(p =0.3,Vector=1:n) Count.location=seq(from=0,to=0,le

13、ngth.out=length(Vector) j<-1 for(i in Vector) path<-sample(c(-1,1),20,replace=TRUE,prob=c(p,1-p)#用-1表示左走，用1表示右走 location<-sum(path) #location代表球向左或向右走|location|步 Count.locationj<-location j<-j+1 hist(Count.location,xlim=c(-20,20),ylim=c(1,2000), main = "高爾頓釘板實驗",ylab="出

14、現(xiàn)的次數(shù)",xlab="球的位置")#畫出直方圖zhixing(p=0.15) #分別執(zhí)行p=0.5，p=0.85#zhixing(p=0.5)#zhixing(p=0.85)zhixing<-function(p =0.3,Vector=1:5000) Count.location=seq(from=0,to=0,length.out=length(Vector) j<-1 for(i in Vector) path<-sample(c(-1,1),20,replace=TRUE,prob=c(p,1-p)#用-1表示左走，用1表示右走 location<-sum(path) #location代表球向左或向右走|location|步 Count.locationj<-location j<-j+1 hist(Count.location,xlim=c(-20,20),ylim=c(1,2000), main = "高爾頓釘板實驗",ylab="出現(xiàn)的次數(shù)",xlab="球的位置")#畫出直方圖 zhixing(Vector=1: