We will compare the distribution of the sample mean from Cauchy distribution and

Question

We will compare the distribution of the sample mean from Cauchy distribution and Uniform(-10, 10) distribution. The command rcauchy generates a sample from Cauchy distribution. (a) Repeat finding the sample mean from iid Cauchy distribution with sample size 10, 10000 times. (sample size is 10, repetition should be made 10000 times) (b) Repeat finding the sample mean from iid Cauchy distribution with sample size 1000, 10000 times. (sample size is 1000, repetition should be made 10000 times) (c) Repeat finding the sample mean from iid Uniform(-10, 10) distribution with sample size 10, 10000 times. (sample size is 10, repetition should be made 10000 times) (d) Repeat finding the sample mean from iid Uniform(-10, 10) distribution with sample size 1000, 10000 times. (sample size is 1000, repetition should be made 10000 times) (e) Report some descriptive statistics and the histograms of sample means in part (a) through (d). (f) Explain your finding in part (e), referencing the relevant page number of the lecture slide. (for example, Chapter x, page xx).

Explanation / Answer

For Cauchy Distribution

(a)

x=rcauchy(10,location=0,scale=10000)
mean(x)
plot(x)

(b)

x=rcauchy(1000,location=0,scale=10000)
mean(x)
plot(x)

(c)

a = -10
b = 10
x = 1000
range = seq(a,b,x)
runif(x,a,b)

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