1) For five distributions below generate a random sample with 50 elements. Const

Question

1) For five distributions below generate a random sample with 50 elements. Construct 5-number summary for each sample. Provide a box-plot.

The distributions: 1) any uniform (discrete or continuous), 2) any symmetric unimodal, 3) any unimodal that is left-skewed, 4) any U-shaped, 5) any symmetric bimodal.

If you use calculators, Excel, MATLAB, or any special statistical software (R, SAS) to do calculations, please provide the supporting materials for your answers. For example, if you do this with Excel, print out the worksheet with formulae. If you use calculators, write done manually how you calculate the characteristics.

The box-plot should be done manually.

Explanation / Answer

First we generate 50 samples observation by using R-software. The command is used is r denote the generating the random number and boxplot is plot by boxplot command.

1) Uniform distribution

x=runif(50,0,1)   ## generate uniform from a=0 to b=1
boxplot(x)

2) any symmetric unimodal is normal distribution

y=rnorm(50,2,0.5)
boxplot(y)

3) any unimodal that is left-skewed is beta distribution

z=rbeta(50,2,3)
boxplot(z)

4) any U-shaped

5) any symmetric bimodal

w=0.5*rnorm(50,-4,2)+0.5*rnorm(50,4,2)
boxplot(w)

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