Use R to answer the following questions: This problem will use R to find all pos

Question

Use R to answer the following questions:

This problem will use R to find all possible orderings of 7 objects, and probabilities associated with them. Consider your vector of possible values to be: values = as.character(1:7)

(a) Use the function sample to draw from values 7 times (without replacement), and return this vector. Notice it is a vector, with 7 values. Display your particular draw.

(b) Repeat (a) 100000 times using an sapply. Notice the result has 7 rows, and 100000 columns, where each column is a specific random draw. Use this result to find how many of your orderings begin with the character 1.

(c) Use your samples from (b) to find the probability that a random ordering started with a 3 and ended with a 7.

(d) The function paste can collapse a vector of many characters into a single character with the following command: one.order = paste(one.draw, collapse = "") Modify the above and use it with an sapply to find how many unique orderings of 7 values there are (assuming order matters and no repetitions are allowed).

Explanation / Answer

a)

values = as.character(1:7)
s1<-sample(values)

s1 is

"7" "4" "1" "3" "6" "5" "2"

b)

t<-sapply(as.data.frame(replicate(100000,values)), sample)

#t is out dataset

> sum(t[1,]=="1")
[1] 14319

so 14319 start with 1

c)

> sum(t[1,] =='3' & t[7,]=='7')
[1] 2294

d)

one.order = apply(t,2, paste, collapse = "")
length(unique(one.order))

we get 5040 unique

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.