Write a program in (mathrm{R}) that simulates 100 samples of size (n) from distributions that are specified

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Write a program in \(\mathrm{R}\) that simulates 100 samples of size \(n\) from distributions that are specified below. Let \(T(F)\) be the variance functional described in Example 9.8. For each sample compute \(T\left(\hat{F}_{n}ight)-T(F)\) and \(\Delta_{1} T\left(F, \hat{F}_{n}-ight.\) \(F)\) where the differential was found in Example 9.8. For each sample size and distribution, construct a scatterplot the 100 values \(T\left(\hat{F}_{n}ight)-T(F)\) and \(\Delta_{1} T\left(F, \hat{F}_{n}-Fight)\). Describe the behavior observed in the plots with relation to the expansion given in Equation (9.1). Use \(n=5,10,25,50\), and 100 .

a. \(\mathrm{N}(0,1)\)

b. Exponential(1)

c. \(\operatorname{UNIFORm}(0,1)\)

d. \(\operatorname{Cauchy}(0,1)\)

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