In this assignment we consider data collected from the donor database of Blood Transfusion Service Center in Hsin-Chu City in Taiwan. The center passes their blood transfusion service bus to one university in Hsin-Chu City to gather blood donated about every three months. The current assignment involves data collected on a random sample of 748 donors. The data was obtained from the UCI Machine Learning Repository. This data was assembled by Prof. I-Cheng Yeh. The file "transfusion.csv" contains the data. The file contains 5 variables: recency = The number of months since the last donation. (numeric) frequency = The total number of donations. (numeric) monetary = Total blood donated (in c.c.). (numeric) time = The number of months since the first donation. (numeric) march2007 = An indicator. Indicates those that donated blood in March, 2007. (factor) In this assignment we consider the variables frequency and monetary. Descriptive Statistics Save the data set in your computer and read it into R. Compute the mean, median, the interquartile range, the standard deviation of the variable frequency and plot it's histogram. In Tasks 1-3 you are asked to describe the distribution of this variable on the basis of the computations and the plot. Estimating Parameters In Tasks 4-6 you are asked to estimate the expectation and standard deviation of the variable frequency. An estimator is used to estimate the expectation. This estimator has a standard deviation. You are required to estimate this standard error, which is the standard deviation of the estimator. You are required to describe which estimator was used for each estimation task. Estimating the MSE Consider the variable monetary. We assume that the distribution of this variable is Exponential() and are interested in the estimation of the parameter . The proposed estimator is 1/X, where X is the sample average. In Tasks 7-8 you are required to estimate the value of the parameter and estimate the mean square error (MSE) of the estimator. You may apply a method called The Bootstrap in order to estimate the MSE. The bootstrap method initiates by estimating the parameter . It proceeds with a simulation to compute the MSE, with equal to the value estimated from the provided data. For the assignment you should complete the following 8 tasks. Tasks 1-3 refer to the descriptive statistics problem presented above, Tasks 4-6 refer to the problem of estimating parameters and Tasks 7-8 refer to the task of estimating the parameter of an Exponential distribution and estimating the MSE of the estimators. Your answers should be short and clear. We recommend that you copy and paste the tasks below into the form titled "Submit your Assignment using this Form". You can then write you answers to the tasks in the designated positions that are marked in the text: Tasks Descriptive Statistics: 1. The distribution of the variable "frequency" is: __ Skewed to the left, __ Symmetric, __ Skewed to the right. Mark the most appropriate option and explain your selection 2. The number of outlier observations in the variable "frequency" is: _____. Explain each step in the computation of the number of outlier observations 3. Which of the following theoretical models is most appropriate to describe the distribution of the variable "frequency"? __ Binomial, __ Poisson, __ Uniform, __ Exponential, __ Normal. Mark the most appropriate option and explain your selection Estimating Parameters: 4. The estimated value of the expectation of the measurement "frequency" is:_____. Explain your answer 5. The estimated value of the standard deviation of the measurement "frequency" is:_____. Explain your answer 6. The estimated value of the standard deviation of the estimator that produced the estimate in 4. is:_____. Explain your answer Estimating the MSE: 7. The estimated value of for the variable "monetary" is:____. Attach the R code for conducting the computation 8. The estimated value of the MSE of the estimator of is:____. Attach the R code for conducting the computation recency frequency monetary time march2007 2 50 12500 98 yes 0 13 3250 28 yes 1 16 4000 35 yes 2 20 5000 45 yes 1 24 6000 77 no 4 4 1000 4 no 2 7 1750 14 yes 1 12 3000 35 no 2 9 2250 22 yes 5 46 11500 98 yes 4 23 5750 58 no 0 3 750 4 no 2 10 2500 28 yes 1 13 3250 47 no 2 6 1500 15 yes 2 5 1250 11 yes 2 14 3500 48 yes 2 15 3750 49 yes 2 6 1500 15 yes 2 3 750 4 yes 2 3 750 4 yes 4 11 2750 28 no 2 6 1500 16 yes 2 6 1500 16 yes 9 9 2250 16 no 4 14 3500 40 no 4 6 1500 14 no 4 12 3000 34 yes 4 5 1250 11 yes 4 8 2000 21 no 1 14 3500 58 no 4 10 2500 28 yes 4 10 2500 28 yes 4 9 2250 26 yes 2 16 4000 64 no 2 8 2000 28 yes 2 12 3000 47 yes 4 6 1500 16 yes 2 14 3500 57 yes 4 7 1750 22 yes 2 13 3250 53 yes 2 5 1250 16 no 2 5 1250 16 yes 2 5 1250 16 no 4 20 5000 69 yes 4 9 2250 28 yes 2 9 2250 36 no 2 2 500 2 no 2 2 500 2 no 2 2 500 2 no 2 11 2750 46 no 2 11 2750 46 yes 2 6 1500 22 no 2 12 3000 52 no 4 5 1250 14 yes 4 19 4750 69 yes 4 8 2000 26 yes 2 7 1750 28 yes 2 16 4000 81 no 3 6 1500 21 no 2 7 1750 29 no 2 8 2000 35 yes 2 10 2500 49 no 4 5 1250 16 yes 2 3 750 9 yes 3 16 4000 74 no 2 4 1000 14 yes 0 2 500 4 no 4 7 1750 25 no 1 9 2250 51 no 2 4 1000 16 no 2 4 1000 16 no 4 17 4250 71 yes 2 2 500 4 no 2 2 500 4 yes 2 2 500 4 yes 2 4 1000 16 yes 2 2 500 4 no 2 2 500 4 no 2 2 500 4 no 4 6 1500 23 yes 2 4 1000 16 no 2 4 1000 16 no 2 4 1000 16 no 2 6 1500 28 yes 2 6 1500 28 no 4 2 500 4 no 4 2 500 4 no 4 2 500 4 no 2 7 1750 35 yes 4 2 500 4 yes 4 2 500 4 no 4 2 500 4 no 4 2 500 4 no 12 4 3 4 4 5 4 2 4 2 2 6 0 3 2 2 4 4 4 4 2 11 2 4 1 2 2 4 2 2 2 2 4 2 4 2 4 2 2 4 2 2 2 2 9 2 2 5 4 4 4 4 6 2 2 2 2 4 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 11 11 4 4 2 4 10 2 4 13 11 4 4 8 11 7 17 9 4 7 8 13 9 5 5 17 8 5 3 10 5 9 5 8 12 24 7 11 7 11 3 5 6 5 4 5 8 4 8 2 5 12 2 6 11 3 5 12 5 2 9 14 3 3 2 3 3 2 2 2 7 6 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10 4 5 6 3 4 4 4 12 8 9 5 4 15 2750 1750 4250 2250 1000 1750 2000 3250 2250 1250 1250 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4 yes 4 yes 4 no 4 yes 4 yes 4 no 24 no 4 no 4 no 4 no 4 yes 4 no 39 no 26 no 63 no 15 no 14 no 43 no 58 no 52 yes 98 no 25 yes 79 yes 11 no 46 no 58 no 86 no 11 no 11 no 11 no 75 no 41 yes 16 yes 59 no 35 no 28 no 37 no 28 no 58 no 41 no 73 yes 23 no 38 yes 58 no 43 yes 23 no 46 no 82 no 21 no 40 no 28 no 16 no 58 no 58 no 46 no 57 no 34 no 78 no 48 no 70 no 22 yes 26 no 16 no 11 11 4 9 14 14 14 16 11 11 11 2 14 14 14 14 14 14 14 2 14 11 4 11 16 16 11 11 12 9 9 4 11 14 11 11 15 9 11 14 16 14 2 14 14 16 14 16 16 11 16 16 11 11 11 9 14 23 11 11 11 11 11 11 11 11 11 11 11 11 16 4 16 14 9 21 14 11 4 21 11 14 23 14 11 16 4 14 4 9 14 11 14 14 14 5 2 2 2 5 3 4 12 4 5 5 4 5 2 2 2 2 2 2 3 6 5 5 3 4 3 5 2 9 1 1 2 2 4 9 5 16 5 4 8 7 2 2 16 4 7 7 6 6 7 2 3 3 7 1 3 4 38 6 1 1 1 1 1 1 1 1 2 5 2 4 2 6 3 2 16 6 2 3 13 6 2 15 4 2 5 2 3 2 4 4 3 5 1 1 1250 500 500 500 1250 750 1000 3000 1000 1250 1250 1000 1250 500 500 500 500 500 500 750 1500 1250 1250 750 1000 750 1250 500 2250 250 250 500 500 1000 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