Empirical probability in R with x1 x2 2 x3

Question

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?

Answer 1

It's easy to duplicate random draws with replicate (here's an example of ten replications):

Rep <- replicate(10, sample(1:10, 3))

Rep

5	7	6	6	1	4	10	7	8	10
7	10	4	10	6	8	2	1	2	8
8	2	5	2	3	9	1	4	1	9

Your inequality's empirical probability can be determined as follows:

set.seed(1222)

Rep <- replicate(100, sample(1:10, 3))

prob1 <- mean(reps[1, ] + reps[2, ] > reps[3, ] * 2)

prob1

0.39

We can produce all 1,000 potential combinations of x1, x2, and x3 just to be sure, because there are only 1,000 possible possibilities.

all.prob <- expand.grid(1:10, 1:10, (1:10) * 2)

probs <- mean(all.probs[,1] + all.probs[,2] > all.probs[,3])

probs

0.475