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# Using the accept-reject algorithm to generate data from beta(2,2) distribution.

M<-3/2

N<-10000

v<-runif(N,0,1)    ## generating candidate data from a uniform distribution
fy.v<-6*v*(1-v)

u<-runif(N,0,1)    
y1<-ifelse(u<fy.v/M,v,NA)  ## flipping a coin with probability fy.v/M to accept

y<-y1[!is.na(y1)]          ## removing those rejected
length(y)/N    ### proportion accepted

mean(y)     ## should be 2/(2+2)
var(y)      ## should be 2*2/((2+2)^2*(2+2+1))
hist(y,nclass=20,freq=FALSE)
t<-c(1:99)/100
lines(t,6*t*(1-t),col=2)