1.Implement a MCM in R to estimate the value of pi as seen here:

https://en.wikipedia.org/wiki/Pi#Monte_Carlo_methods Display the output of your code at N = 20, 100, 200.

2.Compare and contrast von Neumann's random number generator (code is below) with the more modern linear congruential generator (LCG).

List at least 3 differences/similarities.

> vonNeumann <- function(x,n){

+ rx <- NULL

+ d <- max(2,length(unlist(strsplit(as.character(x),""))));

+ getNext <- function(x,d){

+ temp <- x2

+ tbs <- as.numeric(unlist(strsplit(as.character(temp),"")))

+ # to be split

+ tbs_n <- length(tbs);

+ diff_n <- 2*d - tbs_n;

+ dn <- ceiling(d/2)

+ ifelse(diff_n == 0, tbs <- tbs, tbs <- c(rep(0,diff_n),tbs)) + tbs_n <- length(tbs)

+ NEXT <- tbs[-c(1:dn,((tbs_n-dn+1):tbs_n))]

+ return(as.numeric(paste(NEXT,collapse="")))

+}

+ rx[1] <- x

+ for(i in 2:(n+1)) rx[i] <- getNext(rx[i-1],d)

+ return(rx)

+}

> vonNeumann(x=11,n=10)

[1]11121419362984 5 2 0 0 > vonNeumann(x=675248,n=10)

[1] 675248 959861 333139 341914 > vonNeumann(x=8653,n=100) [1] 8653 8744 4575 [30] 2545 4770 7529 [59] 4100 8100 6100 [88] 8100 6100 2100 1354 8333 4388 8100 6100 2100 6100 2100 4100 4100 8100 6100