# Statistics & R Programming Problem

Subject Mathematics Statistics-R Programming

## Question

Check the file: Questions.pdf

## Solution Preview

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set.seed(4)
n <- 300
p <- 0.7
mu1 <- 0
sigma21 <- 1
mu2 <- 5
sigma22 <- 2
x <- ifelse( runif(n)<p, rnorm(n,mu1,sqrt(sigma21)), rnorm(n,mu2,sqrt(sigma22)))

# pdf
f <- function(x,mu1,mu2,sigma21,sigma22,p) {
q <- 1-p
p*dnorm(x,mean=mu1,sd=sqrt(sigma21)) + q*dnorm(x,mean=mu2,sd=sqrt(sigma22))
}

# log likelihood
log.f <- function(x,mu1,mu2,sigma21,sigma22,p) {
sum( log(f(x,mu1,mu2,sigma21,sigma22,p)) )
}...

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