#Math 480 R homework

#The easiest way to get M480pack.txt  is to copy and paste the following 
#command into R.

source("http://parker.ad.siu.edu/Olive/M480pack.txt")

#HW4 6a)

qnorm(p=0.9,mean=100,sd=15)

#HW4 6b)

qnorm(p=0.99,mean=100,sd=15)


#HW7 8a)
#From Olive (2014, 8.1).
#The following commands will plot 4 histograms
#with n =1, 5, 25 and 200. Save the plot in Word.

z1 <- cltsim(n=1)
z5 <- cltsim(n=5)
z25 <- cltsim(n=25)
z200 <- cltsim(n=200)
par(mfrow=c(2,2))
hist(z1$ybar)
hist(z5$ybar)
hist(z25$ybar)
hist(z200$ybar)  #click on R console and hit enter if necessary

#HW7 8b)


z1 <- cltsim2(n=1)
z5 <- cltsim2(n=5)
z25 <- cltsim2(n=25)
z200 <- cltsim2(n=200)
par(mfrow=c(2,2))
hist(z1$ybar,breaks="Scott")
hist(z5$ybar,breaks="Scott")
hist(z25$ybar,breaks="Scott")
hist(z200$ybar,breaks="Scott")
par(mfrow=c(1,1))


#HW8 6)

rwalk(n=100,type=3,y0=1)   

#HW8 7)

poisprocess(n=100, rate=1)



#HW9 3a) 

c1 <- c(0,2/5,1/5,2/5)
c2 <- c(2/5,0,2/5,1/5)
c3 <- c(1/5,2/5,0,2/5)
c4 <- c(2/5,1/5,2/5,0)
P <- cbind(c1,c2,c3,c4)
C <- P
P
for(i in 1:1)
C <- C%*%P   # C = P^2
C

##look at a) output for b)

# HW9 3c)
C <- P
for(i in 1:39)
C <- C%*%P   # C = P^40
C


#HW9 4a)

c1 <- c(0,2/5,1/5,2/5)
c2 <- c(2/5,0,2/5,2/5)
c3 <- c(1/5,2/5,0,1/5)
c4 <- c(2/5,1/5,2/5,0)
P <- cbind(c1,c2,c3,c4)
C <- P
P
for(i in 1:1)
C <- C%*%P   # C = P^2
C

##look at a) output for b)

# HW9 4c)
C <- P
for(i in 1:999)
C <- C%*%P   # C = P^1000
C

#C%*%C - C approx the 0 matrix




#HW10 4

##copy and paste the source command near the top of this file into R

#HW10 4 a)

bmot(n=1000000)

#HW10 4 b)
 
Z <- 1:1000

for(i in 1:1000) Z[i] <- bmot(999)$B[500]
hist(Z)  #Z(500) approx N(0,50) and hist looks like a N(0,50) hist


#HW 11

##copy and paste the source command near the top of this file into R

#HW11 5

#HW11 5a

qcauchy(c(0.025,0.975))

#HW11 5b

out <- rcauchy(1000000)
quantile(out,c(0.025,0.975))

#HW11 5c

shorth3(out)


#HW11 6

u <- rng(n=201)$u
plot(u[-1],u[-201])