1. Central limit theorem [40 marks] For this question, we want to recreate the following graph. Population distribution 1 = 2 1 = 5 1 = 30 Exponential A Uniform M M A U-shaped Normal To do so, we need to find 3 populations with a distribution other than normal distribution and a population with normal distribution. Attached you can find 4 populations with Normal/exponential/Poisson/and uniform distributions. Normal and Uniform populations are just generated distributions while the exponential distribution is actual data for the time between two patient assessment by a physician and the Poisson distribution is the hourly number of arrivals to an ED in Calgary (From my thesis). You can use these distributions or may use any other populations of your choice. However, you need to make sure that you have one normal distribution and 3 non normal distributions. There should be at least 200 observations in the population. If you use other populations and show that they meet the requirements of this problem, there will be 5 bonus mark. If you use the attached populations: no penalty and no bonus. To graphically prove the central limit theorem, you need to use the random sampling technique and take multiple (say 100) samples of sizes 2,5, and 30 of each of the populations. For each population and sample size n:1. 2. 3. Create 100 samples of size n Calculate the mean for each ifthe samples. You will have 100 sample means. Then draw the histogram of these 100 numbers. So, you need to do the above steps 4 (population) x 3 (sample sizes of 2,5,30) or 12 times. In order to create random samples in excel: 1) In each blue cell in each shift copy and paste the following formula: =INDEX($A$2:$A$251, RANDBETWEENH, ROWS($A$2:$A$251)), 1) The first input is the range containing your population data. For me it is column A rows 2 to 251. Make necessary changes so that you are including all the population. Once you are done with randomly selecting your samples, copy them all and paste as values so that they don't change every time you change something in excel. The green cells are the average of the blue column above them. Or, they are the sample means for each of the samples. In each shift, you have 3 green rows, containing the average of your samples with sizes 2, 5, and 30. Draw one histogram for each of them. You can change the number of bins as required. The output of this question: 1. Introduce all 4 populations: what is it about (Generated or a real data)? How many observations? Its mean? What is its distribution. (You need to this step even if you are using the attached populations] Attach your excel le that contains your samples with the pdf file on canvas. You should have a sheet for each population. In the same sheet, there should be all of the samples, one column for each sample size. In the word file create a 4x4 table and copy and paste the histograms from excel in the corresponding cell of the table. Same as the table above