Question

Fill in the blanks in the following simulation for R, which finds the approximate variance of N, the number of rolls of a die needed to get the face having just one dot.

onesixth <- 1/6

sumn <- 0

sumn2 <- 0

for (i in 1:10000) {

n <- 0

while(TRUE) { ________________________________________

if (______________________________ < onesixth) break

}

sumn <- sumn + n

sumn2 <- sumn2 + n^2

}

approxvarn <- ____________________________________________

cat("the approx. value of Var(N) is ",approxvarn,"\n")

Answer 1

Solution:

onesixth <- 1/6

sumn <- 0

sumn2 <- 0

for (i in 1:10000) {

n <- 0

while(TRUE) { n <- n + 1

if (runif(1) < onesixth) break

}

sumn <- sumn + n

sumn2 <- sumn2 + n^2

}

approxvarn <- sumn2/10000 - (sumn/10000)^2

cat("the approx. value of Var(N) is ",approxvarn,"\n")

Sample Output:

the approx. value of Var(N) is  29.28388