Use R code to solve If n = 15 and the data are (5,4, 9,6, 21, 17, 11, 20, 7, 10,

Question

Use R code to solve

If n = 15 and the data are (5,4, 9,6, 21, 17, 11, 20, 7, 10, 21, 15, 13, 16, 8) approxi- mate by simulation the bootstrap estimate of the following estimators: (a) Var(S2) (b) kurtosis is the fourth moment around the mean divided by the square of the variance of the probability distribution minus 3, i.e 4 Ju at it is used to measure the "peakedness" of a probability distribution (c) The skewness of a random variable X is the third standardized moment 3 skewness is a measure of the asymmetry of the probability distribution.

Explanation / Answer

> x=c(5,4,9,6,21,17,11,20,7,10,21,15,13,16,8)
> n=length(x)
> n
[1] 15

> vars2=var(x)
> vars2
[1] 34.31429
> k=((mean(x)^4)/(var(x)^2))-3
> k
[1] 15.81436
> f=mean(((x-mean(x))/sd(x))^3)
> f
[1] 0.1998731

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