Solve Using R code

Here is sample test data.txt

3. The data set _.txt consists of the time that elapsed between when sell orders for stock were placed during April 5, 2010. My hypothesis is that these times have an exponential distribution with CDF F(t) =1-e-At for some unknown rate 1. R has a function pexp that calculates these exponential probabilities. (a) Plot an informative histogram of the data. Use good judgment to choose the number of bins. Be sure to include proper labels and titles. (b) Calculate the MLE, = 7-7, from the data. (c) Use this estimate of to divide the sample space into 10 intervals that will be big enough that the x approximation will be appropriate. (d) Count the number of observations in each of those intervals. You can use the hist, tabulate, or count function. (e) Perform the appropriate x test (f) Inspect the counts and the expected values and give some description of how the data looks different from an exponential distribution. (8) What difference does it make if we used 25 or 100 intervals instead of 10? Experiment a little with different sets of intervals and report the results and whether they demonstrate anything different from the original 10-interval analysis. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 NMNOM 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 0.008354155 0.000576202 0.000853906 4.684308 3.098853 0.07020403 2. 616818 153.4414 0.000501973 0.008068891 41.42738 14.57802 851.3569 121.1605 0.001997165 0.00107185 0.01443074 361. 2978 174.1166 46.51721 1.905224 0.5857393 71.39749 450.9386 9.55276 33.08459 38.20045 76.91316 525. 8071 67.51413 28. 32274 41.5045 102.3815 36.0796 78.118 3.070418 73.94423 7.275958e-12 7.275958e-12 0.005146483 2.065847 0.02142583 0.001043549 4.4976e-05 0.000141811 1.9853e-05 0.000122498 0.000710056 0.000569434 0.00058655 5. 008e-05 0.000230289 0.1725391 0.4502541 0.3108394 6.9606e-05 0.7308778 0.7834382 0.6593845 0.6785249 2.012637 0.2972641 654.4859 514.9598 75.75839 20.69979 7.275958e-12 7.275958e-12 156.9631 65.30435 1055.139 186.0964 7.275958e-12 7.275958e-12 3.458178 0.8312273 7.275958e-12 7.275958e-12 7.953209 7.275958e-12 5.01 3638 4.984931 9.099492 0.9012112 5.004286 3.516813 1.488897 0.001853573 24.63194 44.09532 7.275958e-12 0.4834744 7.275958e-12 0.000421347 0.2298365 0.3541917 0.1745543 0.7985868 119.4979 7.275958e-12 7.275958e-12 1.970638 0.0358541 0.03121543 3.221265 20.58823 16.88414 29.35403 0.7353068 5.662876 2.543461 19.68879 42.9389 47.36758 9.569166 4.009785 26.29533 2.274608 0.3652604 1.044365 532.2455 429.7041 0.00042956 0.787085 0.001572843 0.004779246 279.4728 92.67917 85.88473 0.9367212 0.001142922 488.7987 27.47366 16.56588 0.002710742 0.003283738 7.275958e-12 0.003073443 0.490395 0.000170212 76.44445 3.300119 7.275958e-12 8.104984 20.3714 3.762003 302. 0446 602.4202 95.13743 15.8045 6.092704 0.1676997 0.2716233 0.8072989 0.3686333 230.6561 42.1728 0.2312698 227.433 118.5154 159.773 1123.826 889.827 753.5946 1.116847 0.002714959 0.001084182 0.00098808 0.07413887 0.001929959 0.1233454 0.000999321 0.000291648 9.6141e-05 5.41252-05 1.3363e-05 180.7371 202.2585 9. 201267 11. 20448 14.08667 7.275958e-12 780.927 459.0717 248.5715 146.8505 12.19262 55.49286 565.5437 588.3524 19. 60666 231.7636 289.9507 643.0874 243.487 0.001633732 7.275958e-12 0.000358863 1.6314e-05 9.814001e-06 0.03083047 205. 3481 7.275958e-12 0.000572395 0.4490267 49.79256 236.1506 383.2 0.001572335 0.000219035 0.008211221 0.4634059 7.711e-05 71.1435 0.4642542 6.340187 22.62144 20.55616 0.009499664 14.48547 3.335464 0.4757629 1.607091 7.275958e-12 0.5046051 1. 246978 0.7883012 0.5171066 0.6829509 0.4942509 0.5248902 3. 261193 0.8950864 0.1678422 3.896581 7.275958e-12 0.08705552 1.716091 16.86443 0.001217864 541.889 2231.497 216.1331 0.002058811 0.004856293 0.00035747 0.001142 511 0.6463842 6. 5405e-05 114.6527 3. The data set _.txt consists of the time that elapsed between when sell orders for stock were placed during April 5, 2010. My hypothesis is that these times have an exponential distribution with CDF F(t) =1-e-At for some unknown rate 1. R has a function pexp that calculates these exponential probabilities. (a) Plot an informative histogram of the data. Use good judgment to choose the number of bins. Be sure to include proper labels and titles. (b) Calculate the MLE, = 7-7, from the data. (c) Use this estimate of to divide the sample space into 10 intervals that will be big enough that the x approximation will be appropriate. (d) Count the number of observations in each of those intervals. You can use the hist, tabulate, or count function. (e) Perform the appropriate x test (f) Inspect the counts and the expected values and give some description of how the data looks different from an exponential distribution. (8) What difference does it make if we used 25 or 100 intervals instead of 10? Experiment a little with different sets of intervals and report the results and whether they demonstrate anything different from the original 10-interval analysis. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 NMNOM 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 0.008354155 0.000576202 0.000853906 4.684308 3.098853 0.07020403 2. 616818 153.4414 0.000501973 0.008068891 41.42738 14.57802 851.3569 121.1605 0.001997165 0.00107185 0.01443074 361. 2978 174.1166 46.51721 1.905224 0.5857393 71.39749 450.9386 9.55276 33.08459 38.20045 76.91316 525. 8071 67.51413 28. 32274 41.5045 102.3815 36.0796 78.118 3.070418 73.94423 7.275958e-12 7.275958e-12 0.005146483 2.065847 0.02142583 0.001043549 4.4976e-05 0.000141811 1.9853e-05 0.000122498 0.000710056 0.000569434 0.00058655 5. 008e-05 0.000230289 0.1725391 0.4502541 0.3108394 6.9606e-05 0.7308778 0.7834382 0.6593845 0.6785249 2.012637 0.2972641 654.4859 514.9598 75.75839 20.69979 7.275958e-12 7.275958e-12 156.9631 65.30435 1055.139 186.0964 7.275958e-12 7.275958e-12 3.458178 0.8312273 7.275958e-12 7.275958e-12 7.953209 7.275958e-12 5.01 3638 4.984931 9.099492 0.9012112 5.004286 3.516813 1.488897 0.001853573 24.63194 44.09532 7.275958e-12 0.4834744 7.275958e-12 0.000421347 0.2298365 0.3541917 0.1745543 0.7985868 119.4979 7.275958e-12 7.275958e-12 1.970638 0.0358541 0.03121543 3.221265 20.58823 16.88414 29.35403 0.7353068 5.662876 2.543461 19.68879 42.9389 47.36758 9.569166 4.009785 26.29533 2.274608 0.3652604 1.044365 532.2455 429.7041 0.00042956 0.787085 0.001572843 0.004779246 279.4728 92.67917 85.88473 0.9367212 0.001142922 488.7987 27.47366 16.56588 0.002710742 0.003283738 7.275958e-12 0.003073443 0.490395 0.000170212 76.44445 3.300119 7.275958e-12 8.104984 20.3714 3.762003 302. 0446 602.4202 95.13743 15.8045 6.092704 0.1676997 0.2716233 0.8072989 0.3686333 230.6561 42.1728 0.2312698 227.433 118.5154 159.773 1123.826 889.827 753.5946 1.116847 0.002714959 0.001084182 0.00098808 0.07413887 0.001929959 0.1233454 0.000999321 0.000291648 9.6141e-05 5.41252-05 1.3363e-05 180.7371 202.2585 9. 201267 11. 20448 14.08667 7.275958e-12 780.927 459.0717 248.5715 146.8505 12.19262 55.49286 565.5437 588.3524 19. 60666 231.7636 289.9507 643.0874 243.487 0.001633732 7.275958e-12 0.000358863 1.6314e-05 9.814001e-06 0.03083047 205. 3481 7.275958e-12 0.000572395 0.4490267 49.79256 236.1506 383.2 0.001572335 0.000219035 0.008211221 0.4634059 7.711e-05 71.1435 0.4642542 6.340187 22.62144 20.55616 0.009499664 14.48547 3.335464 0.4757629 1.607091 7.275958e-12 0.5046051 1. 246978 0.7883012 0.5171066 0.6829509 0.4942509 0.5248902 3. 261193 0.8950864 0.1678422 3.896581 7.275958e-12 0.08705552 1.716091 16.86443 0.001217864 541.889 2231.497 216.1331 0.002058811 0.004856293 0.00035747 0.001142 511 0.6463842 6. 5405e-05 114.6527