For the following problem, you must create your Excel file from scratch. You mus

Question

For the following problem, you must create your Excel file from scratch. You must show all your work and logic. It must contain the formulas, so it can be expanded for more runs. X, Y, Z, are three given uncorrelated random variables with following characteristics: a) Variable X is normally distributed with mean 100 and variance 400. b) Variable Y is discrete uniformly distributed with a probability distribution given by p(y) = 0.2 with y = 0, 1, 2, 3, and 4. c) Variable Z is distributed in accordance with the following table: Use a sample of size 100 to build a simulation in excel to estimate the mean of a new variable V, that is defined as: D = (X - 25Y)/(2Z)

Explanation / Answer

This is my Random Sampling

Where X = =NORMINV(RAND(),100,20)

Y = I have randomized 20 values of 0,1,2,3 and 4

Z = I have used randomized 10 values of Z= 10 , 25 values of Z= 20 , 50 values of Z = 30 and 15 values of Z = 40

then D = (X- 25Y)/ (2D) formula in D column. the result is given here

And average of simulation is E[V] = 1.3342

X Y Z D 111.0746 1 20 2.151865 109.0093 0 10 5.450466 77.95777 4 30 -0.36737 107.5755 3 30 0.542925 90.80557 2 30 0.680093 100.1098 2 30 0.835164 130.1937 1 20 2.629843 106.3398 0 10 5.316991 101.0425 4 40 0.013031 73.1955 4 40 -0.33506 90.16061 2 30 0.669344 65.80597 1 20 1.020149 102.2905 0 20 2.557263 78.4856 3 30 0.058093 129.7557 3 30 0.912596 112.5468 2 30 1.042446 75.97522 4 40 -0.30031 92.82673 2 30 0.713779 112.5013 2 30 1.041688 103.653 2 30 0.894216 90.75938 1 30 1.09599 121.9435 1 20 2.423589 105.8907 0 20 2.647267 103.2821 4 40 0.041026 147.96 2 30 1.632667 100.483 0 10 5.024152 92.05933 4 40 -0.09926 83.4834 4 40 -0.20646 74.12556 4 30 -0.43124 112.2306 4 40 0.152882 121.3074 1 20 2.407684 83.77717 0 20 2.094429 104.5038 3 30 0.49173 67.76291 1 20 1.069073 89.49883 3 30 0.241647 64.22788 0 20 1.605697 107.6986 1 20 2.067465 88.4096 2 30 0.64016 78.25757 2 30 0.470959 111.6346 1 20 2.165865 70.69764 4 40 -0.36628 103.2297 1 30 1.303828 101.6237 1 20 1.915593 104.9865 0 10 5.249327 70.57581 3 30 -0.07374 76.92698 1 20 1.298174 84.67354 3 30 0.161226 93.66201 0 10 4.6831 121.6042 4 30 0.36007 99.51652 1 30 1.241942 122.4601 0 20 3.061503 115.2924 3 30 0.671539 97.93046 1 20 1.823261 140.042 4 40 0.500525 117.3083 0 20 2.932708 91.36151 1 20 1.659038 81.90204 0 10 4.095102 104.6364 2 30 0.910607 116.459 4 30 0.274317 117.4529 2 30 1.124215 83.06704 3 30 0.134451 114.7138 0 20 2.867844 88.33961 2 30 0.638993 88.15171 1 20 1.578793 103.7543 2 30 0.895905 102.9311 4 40 0.036639 95.29568 4 40 -0.0588 78.52723 0 10 3.926361 103.3496 4 40 0.04187 114.2687 1 30 1.487812 108.9198 2 30 0.981997 121.9937 3 30 0.783228 77.26914 3 30 0.037819 87.5539 4 40 -0.15558 77.76799 0 20 1.9442 102.4553 0 10 5.122767 105.31 3 30 0.505166 102.8601 1 20 1.946503 120.9978 2 30 1.183296 86.0889 2 30 0.601482 110.9081 0 10 5.545403 85.50487 3 30 0.175081 83.36797 2 30 0.556133 104.8876 2 30 0.914794 131.8837 3 30 0.948062 111.7795 1 20 2.169488 87.92048 3 30 0.215341 83.88349 0 20 2.097087 94.87499 0 20 2.371875 138.1195 2 30 1.468659 168.2535 4 40 0.853169 72.10722 3 30 -0.04821 139.5947 4 30 0.659912 85.38086 1 30 1.006348 86.91063 3 30 0.198511 72.8509 3 30 -0.03582 69.53261 4 40 -0.38084 94.43453 3 30 0.323909 114.9096 0 10 5.745478 90.16442 3 30 0.25274 Average 99.43828 2 27 1.334265

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