College of Engineering GENG 200 Probability and Statistics for Engineers Spring 2016 Computer\tBased\tAssignment\t#1 [the\twork\tmust\tbe\tdone\tusing\tappropriate\tsoftware\twhich\tchoice\tis\tleft\tto\tstudents] Given\t11/23/16\tdue\ton\t12/03/16 Exercise\t#\t1 Plot\tthe\tprobability\tmass\tfunction\t(PMF)\tand\tthe\tcumulative\tdistribution\tfunction\t(CDF)\tof\t3\trandom variables following (1) binomial distribution [p,n], (2) a geometric distribution [p], and (3) Poisson distribution\t[].\tYou\thave\tto\tconsider\ttwo\tsets\tof\tparameters\tper\tdistribution\twhich\tcan\tbe\tchosen arbitrarily. The\tfollowing\tsteps\tcan\tbe\tfollowed: Setp1: Establish\ttwo\tsets\tof\tparameters\tof\tthe\tdistribution\t: For\tGeometric\tand\tPoisson\tdistributions take\ttwo\tvalues\tof\tp\t(p1\tand\tp2)\tand\ttake\ttwo\tvalues\tof\t[]. (1\tand\t2)\trespectively. For\tthe\tbinomial you\tshould\ttake\ttwo\tvalues\tof\tp\tand\ttwo\tvalues\tof\tn,\tfirst\tkeep\tp\tfixed\tand\tchange\tn,\tin\tthe\tsecond keep\tn\tfixed\tand\tchange\tp. Step\t2:\tGenerate\tthe\trandom\tvariables\t(at\tleast\t10\tvalues)\t[column\t1] Step\t3:\tCalculate\tthe\tPMF\t[column\t2]\tand\tCDF\t[column\t3] Step\t4:\tPlot\tthe\tPMF\tand\tCDF\tin\tdifferent\tgraphics\t(It\tis\trecommended\tto\tcombine\tthe\tgraphics\twhile changing\tthe\tparameters.) Comment\ton\thow\tthe\tparameters\tvalues\taffect\tthe\tdistribution. Exercise # 2:A- Cotton fibers are classified into three groups based on their staple length which is average length of the fibers making up a sample: Long-staple cotton (with length above 33 mm), medium-staple cotton (with length 20 to 33mm) and short-staple cotton (with length less than 20mm). The distribution of staple length is normal with mean 25mm, and standard deviation 5mm. Draw a normal distribution graph and show these proportions in different colors in the same graph. The above graph can be generated using any software. For excel user you can follow the below steps: Step 1: Generate the random variables (at least 40values) in a column. Step 2: Determine the height of the bell shaped curve at the values of random variables in step 1. (Excel users can use the function norm.dist) Step 3: Use appropriate graphics to plot the bell shaped curve in step 2 and to show the corresponding areas for each of the three categories with different colors in the same plot. (Hint: For each of the three categories, use logical function to identify relevant ranges of column generated in step 2 and show the corresponding areas in plot obtained in Step 3 using different colors. B-Make a search on the literature and present proof of at least 3 practical and real random variables following normal distribution