Hallo
 
I would appreciate any help with the following. 
Problem: Suppose A, B and C are independent U(0,1) random variables. What is the probability that A(x^2) + Bx + C has real roots?
I have done the theoretical work and obtained an answer of 1/9 = 0.1111.
Now I want to show my students to get this in R with simulation.
Below are two attemps, both giving the answer to be about 0.26.
 
Could anybody please help me with providing a more elegant way to do this? (I am still learning R and trying to get my students to learn it as well. I know there must be a better way to get this.) I must be doing something wrong ?
 
n <- 10000
### Method 1 ###
cnt <- rep(0,n)
for (i in (1:n)) {
   a <- runif(1)
   b <- runif(1)
   c <- runif(1)
   cnt[i] <- ifelse(((b^2)>4*a*c),1,0)
}
sum(cnt)/n
### Method 2 ###
one.s <- function(x) {
  ret <- ifelse(((x[2]^2) > 4 * x[1] * x[3]),1,0)
  ret
}
m <- cbind(runif(n),runif(n),runif(n))
sum(apply(m,1,one.s))/n
######
 
THANK YOU.
Jacob L van Wyk
Dept of Statistics
University of Johannesburg
P O Box 524
Auckland Park 2006
South Africa
Tel: +27-11-559-3080
Fax: +27-11-559-2832
Cell: +27-82-859-2031

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