Lab 4 This assignment is due before the end of your Monday/Tuesday section. For every section you will submit your handwritten work to your TA. Only neat and organized assignments will be graded for credit. Take pride in all of your work. Note: you may print plots for your assignment or you can just demonstrate to your TA during section that you can create plots. 1. Use the Number Generator on the Analysis Toolpak to Generate 1000 random numbers from a Normal distribution with mean 3 and variance 4. (a) Draw a histogram. (b) Compute the sample mean and compare with E[X] = 3. (c) Compute the sample standard deviation and compare with SD[X] = 2. 2. We want to generate a random sample from Exponential () distribution, but it is not available on the Excel Data Analysis package. So we use the following device. 1 It is known that if U has Uniform(0, 1) distribution, then ln(U ) has exponential 1 distribution with mean . (a) Use this idea to generate 1000 random numbers from an Exponential distribution with rate = 0.5. Note that the mean is 2 and the variance is 4. First generate 1000 random numbers from Uniform(0, 1) in column A. Then type ln =-2*LN(A1) in cell B1. Drag and ll B2 to B1000. (b) Compute the mean and compare with E[X] = 2. (c) Compute the standard deviation and compare with SD(X) = 2. 3. Use the Excel Data Analysis package to generate 2000 random numbers from Uniform (-2, 4). (a) Draw a histogram. (b) Compute the mean and compare with E[X] = a+b 2 = 1. ? (c) Compute the variance and compare with Var[X] = (ba)2 12 =3 (d) The uniform random numbers can also be generated according to the formula =(6*RND())-2. Briey explain why this formula works