模拟单个n侧模具，其中具有最高编号的一侧显示的频率是所有其他侧面的两倍

Question

I need to do this assignment. I just don't know how it works. The question is.

Modify the function roll() from the lecture in a way that it simulates a single n-sided die where the side with the highest number shows up twice as often as all other sides. Functions you may find useful are ?, c(), min(), max(), length(), sort() and rep().

And the function goes.

roll <- function( num = 1:6, rolls = 1) {
  dice <- sample(num, size = rolls, replace = TRUE)
  return(dice)
}

I'm pretty sure that i have to use the 'prob'-parameters in the sample-Function but i don't know how.

Answer 1

You can do it without the prob argument by thinking about what kind of fairly-weighted (all faces equally probable) die would give the results you want.

sample(1:6, 1) gives you a single sample from an unbiased six-sided die. What you seem to want in this instance is equivalent to a seven-sided die with two sixes. Which would be...

sample(c(1:6,6),1)

That's an equal change of 1 to 5, and double the chance of a 6.

> table(sample(c(1:6,6),7000,replace=TRUE))

   1    2    3    4    5    6 
 972 1018 1016  980 1018 1996 

Its not clear to me whether "the highest number shows up twice as often as all other sides" means "all the other sides put together". In which case you want to sample from a 10-sided die with 1 to 5 plus 5 sixes:

sample(c(1:5, rep(6,5)),1)

That's an equal chance of either getting 1 to 5 OR 6.

> table(sample(c(1:5, rep(6,5)),10000,replace=TRUE))

   1    2    3    4    5    6 
1012  961  943 1018 1026 5040

Generalise to N and write your function.

Answer 2

You are right, the prob -Parameter is useful here (eventhough you could do without).

Here are the steps you have to complete:

• Find out which of the entries in num is largest (dont assume that it is the last)
• You need the index (="position") of that entry.
• Calculate which probability each entry except the largest one would have. Example: If n=6 then each prob is 1/7 with the exception of the last which has 2/7.
• Make a vector containing these probabilities in the right positions. You already know the position of the largest, so you would put the doubled prob in that position.
• Give the prob to sample () .
• Test! Run it many times to find out if the largest is really approx. double as often.