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
[[alternative HTML version deleted]]
______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
