1hr 2hr 6hr 12hr 18hr 24hr 48hr 72hr 1 53.2 102.2 261.2 474.9 651.9 805.3 1163.7
ID: 3305918 • Letter: 1
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1hr 2hr 6hr 12hr 18hr 24hr 48hr 72hr 1 53.2 102.2 261.2 474.9 651.9 805.3 1163.7 1388.3 2 85.2 122 205.3 371.6 434.7 489.9 604.7 612.6 3 55.4 72.7 198.8 309.1 374.6 423.7 491 567.3 4 112 181.8 295.9 385.8 414.9 429.9 443.3 478 5 69.7 83.5 236.4 352.6 394.6 432.6 587.3 611.8 6 94.2 127.2 152.9 157.1 157.1 163.9 197.6 213.6 7 78 92.5 155.4 205.9 252.6 296.1 357.3 410.2 8 54.2 89.5 204.6 327.1 398.7 439.8 483.5 507.7 9 54 101.6 201.5 269.5 313.8 388.5 627.2 693.5 10 102.4 140.7 338.9 664.9 967.7 1151.9 1609.2 1703.2 11 45.7 67.7 146.1 189.7 235.6 284.2 423.7 638.3 12 52.1 79.9 181.1 216.5 237.1 247.9 393.5 451.7 13 72.9 99.9 157.5 277.2 361 434.2 468.7 495.5 14 42.3 46.4 83.4 136.6 173.8 184.5 227.1 276.5 15 33.6 53.3 121.3 227.7 304.3 383.4 516.5 654.1 16 38.1 62.7 79.6 100.8 111 120.4 176.8 208.2 17 42.2 71.9 157.1 276.3 402.3 465.1 587.5 631.1 18 52.3 58.3 81.5 132.1 152.7 175.2 224.7 235.3 19 57.2 95.6 250.5 396.6 433.6 474.2 580.5 656.2 20 54.8 109.1 312.6 529.5 617.3 653.6 722.7 744.6 21 57.1 97.9 234 391.8 524.6 730 914 920.9 22 33.6 57 103.4 158.1 179.1 206.8 343.7 408.5 23 63 97.5 250 466.5 610 677.5 778 835 24 77 144 329.5 545.5 716 862 1170.5 1270.5 25 55 77 160.5 235.5 265.5 284 325.5 374 26 31.5 53 112.5 158.5 177 192 264 314.5 27 56 102 237 368 513.5 607.5 767.2 774.2 28 62.5 101.5 200.5 297.5 371.5 466.5 552.5 552.5 29 71 119.5 299.5 467 549 558.5 634 714 30 66 128 240.5 345 421.5 457 497 524 31 58.5 113 233.5 365.5 448.5 497 918.5 1021 32 65.5 109 206 286.5 291.5 292.5 383 402.5 33 50.5 70 147 277.5 361.5 427 573 672.5 34 44.5 75.5 182 271 357.5 397.5 513 652 35 51.5 93.5 218.5 363 410 440.5 541 642 36 48 71.5 147 265.5 329.5 362 482.5 493.5 37 60.5 104.5 166.5 205 219.5 221 261.5 295.5 38 65.5 120.5 292.5 445.5 474 476 488.6 493.7 Water Resources Engineering BSE 2031 (2017) Rainfall Frequency Analysis Annual maximum rainfalls (in mm) of various durations of the Bamboo lakeare listed in the file BambooLake_AMS.csv. (1) Conduct goodness-of-fit test (the Kolmogorov-Smirnov test and chi-square test) to 1. determine whether the annual maximum rainfalls at thecan be characterized by Pearson type III distribution. Estimate distribution parameters by the method of maximum likelihood. [Note: Assume annual maximum rainfalls can be characterized by the Pearson type III distribution and use (in -5) as the location parameter(min is the lowest observed value)] (2) (3) Plot the depth-duration-frequency (DDF) curve and the intensity-duration-frequency (IDF) curve Fit the IDF curve by using the following model (4) aT" (tr + by i(tr,T) = with b=0 .Explanation / Answer
Rolling a single die
1) probability of rolling divisors of 6 :
Since its a single die, the possible outcomes are 1,2,3,4,5,6. All have equal probability(1/6) since its a fair die
Out of these divisors of 6 are 1,2,3,6. So P(divisors of 6) = 1/6*1/6*1/6*1/6 = 1/1296 = 0.0008
2) probability of rolling a multiple of 1: Since all(1,2,3,4,5,6) are multiples of 6 = 1/6*1/6*1/6*1/6*1/6*1/6= 1/46656 = 0.00002
3) probability of rolling an even number : There are 3 even numbers between 1-6 i.e. 2,4,6
Hence probability of rolling an even number = 1/6*1/6*1/6 = 1/216 =0.0046
4) List of all possible outcomes of rolling a single die ={1,2,3,4,5,6}
5) probability of rolling factors of 3 : Factors of 3 are 1,3
Hence probability of rolling factors of 3 = 1/6*1/6 = 1/36 = 0.0278
6) probability of rolling a 3 or smaller : 3 or smaller are 1,2,3. Hence the probability = 1/6*1/6*1/6 = 1/216 = 0.0046
7) probability of rolling a prime number: Prime numbers between 1-6 are 2,3,5 hence probability = 1/6*1/6*1/6=1/216=0.0046
8) probability of rolling factors of 4 : Factors of 4 are 1,2,4 hence the probability = 1/6*1/6*1/6 = 1/216 =0.0046
9) probability of rolling divisors of 30 : Divisors of 30 are 1,2,3,5,6 = 1/6*1/6*1/6*1/6*1/6 = 1/7776 = 0.0001
10) probability of rolling factors of 24: Factors of 24 are 1,2,3,4,6 = 1/6*1/6*1/6*1/6*1/6=1/7776=0.0001
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