Question

Statistics and probability in R

D1 is a fair dice

1)build the pmf table in R

2)find the varience using formual E[D1- − µ]^2 and shortcut formula E[D^2 ] − [E(D)]^2 = E[D^2 ] − µ^2 in R

3)find the standard deviation in R

I'm looking for the R code to learn how to do it.

Answer 1

The sample space for one throw of a 6 sided fair die is .

Each outcome is equally likely with probability .

1) The PMF table is

	1	2	3	4	5	6

2) The varianc is defined as

Here,

The second moment is

The R code for finding variance and standard deviation is given below

D <- c(1,2,3,4,5,6)
p <- 1/6
ED <- sum (p*D)
ED2 <- sum (p*D^2)
VD1 <- sum (p*(D-ED)^2)
VD2 <- ED2 - ED^2
SD <- sqrt(VD1)
VD1
VD2
SD

The output is

> VD1
[1] 2.916667
> VD2
[1] 2.916667
> SD
[1] 1.707825

3) Testandard devbaition is .