I have a question - how to generate 100 times a vector of 3 random numbers (x1, x2, x3) from 1 to 10 so I can find the empirical probability of x1+x2>2*x3? I know how to generate 3 random numbers from 1 to 10 with sample(1:10, 3) but how to do this n times?
Thanks in advance
It's simple to repeat random draws with replicate (here showing 10 replications):
reps <- replicate(10, sample(1:10, 3))
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] 9 1 6 8 3 1 10 7 1 2
[2,] 8 9 10 2 4 7 5 3 5 5
[3,] 1 8 4 6 7 2 7 5 3 9
The empirical probability of your inequality can be calculated:
set.seed(1222)
reps <- replicate(100, sample(1:10, 3))
prob <- mean(reps[1, ] + reps[2, ] > reps[3, ] * 2)
[1] 0.39
Just for completeness, because there are only 1,000 possible combinations of x1, x2, and x3, we can generate all of them and calculate the exact probability:
all.probs <- expand.grid(1:10, 1:10, (1:10) * 2)
prob <- mean(all.probs[,1] + all.probs[,2] > all.probs[,3])
[1] 0.475