Q6. (18pts). (Your solution should include R code and R output. R markdown should be used...

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Q6. (18pts). (Your solution should include R code and R output. R markdown should be used to present your solution) Exponential distribution is one continuous distribution with one parameter A. The expected value and variance of exponential random variable are: = 1/A, 1 12 One population follows exponential distribution with parameter = 10. Draw k random samples (sample size is n) from this population, calculate the sample means, and plot the histogram for the sample means. Hint: x = rexp(n, rate = 10) is the R code to create a random sample (sample size n) from an exponential distribution with A = 10. 1.(3pts) Let k 1000, n = 3. = 2.(3pts) Let k 1000, n = 10. = 3.(3pts) Let k 1000, n = 1000. = 4.(3pts) Compare 1, 2, and 3. which histogram is closer to normal distribution (symmetric bell shape)? Is the result related to the sample size n? 5.(3pts) Let k = 1000, n = 10 compute sample mean and sample variance for X. 6.(3pts) Compare the results from 5 with the underline population mean and variance. Do they follow the proposition E(X) = V(X) = o/n? Q6. (18pts). (Your solution should include R code and R output. R markdown should be used to present your solution) Exponential distribution is one continuous distribution with one parameter A. The expected value and variance of exponential random variable are: = 1/A, 1 12 One population follows exponential distribution with parameter = 10. Draw k random samples (sample size is n) from this population, calculate the sample means, and plot the histogram for the sample means. Hint: x = rexp(n, rate = 10) is the R code to create a random sample (sample size n) from an exponential distribution with A = 10. 1.(3pts) Let k 1000, n = 3. = 2.(3pts) Let k 1000, n = 10. = 3.(3pts) Let k 1000, n = 1000. = 4.(3pts) Compare 1, 2, and 3. which histogram is closer to normal distribution (symmetric bell shape)? Is the result related to the sample size n? 5.(3pts) Let k = 1000, n = 10 compute sample mean and sample variance for X. 6.(3pts) Compare the results from 5 with the underline population mean and variance. Do they follow the proposition E(X) = V(X) = o/n?