Suppose that the probability distribution for a population is a Poisson distribution with A = 4 (average rate of occurrence). It has a population mean 4 and standard deviation 2. Generate 300 samples of size 1, 10, and 30 from Poisson population with A = 4. (Please note that you may have noticed "" as Poisson parameter in the lecture note which has the same meaning as "" ) (a) Use EXCEL to calculate the mean and standard deviation of the sample means and include your outputs. (b) Use EXCEL to draw histogram of the sample means of size 1, 10 and 30 and include your outputs. Do they look mound shaped? Why or why not? (c) Find the theoretical mean and standard deviation of the statistics involved in (a). Compare the mean and standard deviation of each generated empirical distribution with those of the respective theoretical distributions. Fill out the following table: Distribution Theoretical Empirical (Approx.) In X10 10 X30 30 EXCEL Instructions . Generation of Samples: Sample Size 1: Data > Data Analysis > Random Number Generation > OK > Type the following parameters: Number of Variables (1), Number of Random Numbers (300), Distribution (Poisson), Parameters () = 4) > OK. Sample Sizes 10, 30: Repeat the above steps in separate worksheets to gener- ate samples of size 10 and 30 by changing the "Number of Variables" argument only. . Sample Means: Type "=AVERAGE(Data Range)" in the desired cell and hit Enter. Now hover over the bottom right corner of the cell until a tiny "+" (fill handle) appears and drag the formula down 300 cells. . Descriptive Statistics (Mean and Standard Deviation): Select data ("Data Range" ) > Data > Data Analysis > Descriptive Statistics > OK > Select the Data by clicking on "1" of the Input Range (or select Data Range) > "Summary Statistics" > OK. . Histogram: Select data ("Data Range") > Insert > Insert Statistics Chart > Histogram > Double click on chart title and give an appropriate title