QUESTION 1

a) P=0.05, n=5

BINOMIAL DISTRIBUTION POISSON DISTRIBUTION NORMAL DISTRIBUTION

P=0.05, n=10

BINOMIAL DISTRIBUTION POISSON DISTRIBUTION NORMAL DISTRIBUTION

X P(X=x)0 0.7737811 0.2036272 0.0214343 0.0011284 2.97E-055 3.13E-07

X P(X=x)0 0.7788011 0.19472 0.0243383 0.0020284 0.0001275 6.34E-06

X P(X=x)0 0.7176851 0.2504852 0.0012973 9.97E-084 1.14E-135 1.92E-21

X P(X=x)0 0.4449141 0.4449142 0.0541963 0.0008044 1.45E-065 3.2E-106 8.58E-157 2.8E-208 1.12E-269 5.41E-34

10 3.19E-42

X P(X=x) 0 0.6065311 0.3032652 0.0758163 0.0126364 0.001585 0.0001586 1.32E-057 9.4E-078 5.88E-089 3.26E-09

10 1.63E-10

X P(X=x) 0 0.5987371 0.3151252 0.0746353 0.0104754 0.0009655 6.09E-056 2.67E-067 8.04E-088 1.59E-099 1.86E-11

10 9.77E-14

P=0.05, n=20

BINOMIAL DISTRIBUTION POISSON DISTRIBUTION NORMAL DISTRIBUTION

X P(X=x) X P(X=x) X P(X=x)0 0.358486 0 0.367879 0 0.2418091 0.377354 1 0.367879 1 0.4093062 0.188677 2 0.18394 2 0.2418093 0.059582 3 0.061313 3 0.0498594 0.013328 4 0.015328 4 0.0035885 0.002245 5 0.003066 5 9.01E-056 0.000295 6 0.000511 6 7.9E-077 3.11E-05 7 7.3E-05 7 2.42E-098 2.66E-06 8 9.12E-06 8 2.58E-129 1.87E-07 9 1.01E-06 9 9.62E-16

10 1.08E-08 10 1.01E-07 10 1.25E-1911 5.17E-10 11 9.22E-09 11 5.68E-2412 2.04E-11 12 7.68E-10 12 9E-2913 6.61E-13 13 5.91E-11 13 4.98E-3414 1.74E-14 14 4.22E-12 14 9.61E-4015 3.66E-16 15 2.81E-13 15 6.47E-4616 6.02E-18 16 1.76E-14 16 1.52E-5217 7.46E-20 17 1.03E-15 17 1.25E-5918 6.54E-22 18 5.75E-17 18 3.58E-6719 3.62E-24 19 3.02E-18 19 3.58E-7520 9.54E-27 20 1.51E-19 20 1.25E-83

b) P=0.1, n=5

BINOMIAL DISTRIBUTION POISSON DISTRIBUTION NORMAL DISTRIBUTION

X P(X=x) X P(X=x) X P(X=x)0 0.59049 0 0.606531 0 0.4504711 0.32805 1 0.303265 1 0.4504712 0.0729 2 0.075816 2 0.0488163 0.0081 3 0.012636 3 0.0005734 0.00045 4 0.00158 4 7.3E-075 0.00001 5 0.000158 5 1.01E-10

P=0.1, n=10

BINOMIAL DISTRIBUTION POISSON DISTRIBUTION NORMAL DISTRIBUTION

X P(X=x) X P(X=x) X P(X=x)0 0.348678 0 0.367879 0 0.2412761 0.38742 1 0.367879 1 0.4205242 0.19371 2 0.18394 2 0.2412763 0.057396 3 0.061313 3 0.0455714 0.01116 4 0.015328 4 0.0028335 0.001488 5 0.003066 5 5.8E-056 0.000138 6 0.000511 6 3.91E-077 8.75E-06 7 7.3E-05 7 8.67E-108 3.65E-07 8 9.12E-06 8 6.33E-139 9E-09 9 1.01E-06 9 1.52E-16

10 1E-10 10 1.01E-07 10 1.2E-20

P=0.1, n=20

BINOMIAL DISTRIBUTION POISSON DISTRIBUTION NORMAL DISTRIBUTION

X P(X=x) X P(X=x) X P(X=x)0 0.121577 0 0.135335 0 0.0978831 0.27017 1 0.270671 1 0.2252382 0.28518 2 0.270671 2 0.2973633 0.19012 3 0.180447 3 0.2252384 0.089779 4 0.090224 4 0.0978835 0.031921 5 0.036089 5 0.0244056 0.008867 6 0.01203 6 0.0034917 0.00197 7 0.003437 7 0.0002878 0.000356 8 0.000859 8 1.35E-059 5.27E-05 9 0.000191 9 3.64E-07

10 6.44E-06 10 3.82E-05 10 5.65E-0911 6.51E-07 11 6.94E-06 11 5.02E-1112 5.42E-08 12 1.16E-06 12 2.56E-1313 3.71E-09 13 1.78E-07 13 7.5E-1614 2.06E-10 14 2.54E-08 14 1.26E-1815 9.15E-12 15 3.39E-09 15 1.21E-2116 3.18E-13 16 4.24E-10 16 6.71E-2517 8.31E-15 17 4.99E-11 17 2.13E-2818 1.54E-16 18 5.54E-12 18 3.87E-3219 1.8E-18 19 5.83E-13 19 4.05E-3620 1E-20 20 5.83E-14 20 2.42E-40

P=0.5, n=5

BINOMIAL DISTRIBUTION POISSON DISTRIBUTION NORMAL DISTRIBUTION

X P(X=x) X P(X=x) X P(X=x)0 0.03125 0 0.082085 0 0.029291 0.15625 1 0.205212 1 0.1450742 0.3125 2 0.256516 2 0.3228693 0.3125 3 0.213763 3 0.3228694 0.15625 4 0.133602 4 0.1450745 0.03125 5 0.066801 5 0.02929

P=0.5, n=10

BINOMIAL DISTRIBUTION POISSON DISTRIBUTION NORMAL DISTRIBUTION

X P(X=x) X P(X=x) X P(X=x)0 0.000977 0 0.006738 0 0.00171 0.009766 1 0.03369 1 0.0102852 0.043945 2 0.084224 2 0.0417073 0.117188 3 0.140374 3 0.1133724 0.205078 4 0.175467 4 0.2065775 0.246094 5 0.175467 5 0.2523136 0.205078 6 0.146223 6 0.2065777 0.117188 7 0.104445 7 0.1133728 0.043945 8 0.065278 8 0.0417079 0.009766 9 0.036266 9 0.010285

10 0.000977 10 0.018133 10 0.0017

P=0.5, n=20

BINOMIAL DISTRIBUTION POISSON DISTRIBUTION NORMAL DISTRIBUTION

X P(X=x) X P(X=x) X P(X=x)0 9.53674E-07 0 4.53999E-05 0 8.10005E-061 1.90735E-05 1 0.000453999 1 5.41559E-052 0.000181198 2 0.002269996 2 0.0002964463 0.001087189 3 0.007566655 3 0.0013285734 0.004620552 4 0.018916637 4 0.0048749195 0.014785767 5 0.037833275 5 0.0146450366 0.036964417 6 0.063055458 6 0.0360209167 0.073928833 7 0.090079226 7 0.0725371268 0.120134354 8 0.112599032 8 0.1195933949 0.160179138 9 0.125110036 9 0.161434109

10 0.176197052 10 0.125110036 10 0.1784122511 0.160179138 11 0.113736396 11 0.16143410912 0.120134354 12 0.09478033 12 0.11959339413 0.073928833 13 0.072907946 13 0.07253712614 0.036964417 14 0.052077104 14 0.03602091615 0.014785767 15 0.03471807 15 0.01464503616 0.004620552 16 0.021698794 16 0.00487491917 0.001087189 17 0.012763996 17 0.00132857318 0.000181198 18 0.007091109 18 0.00029644619 1.90735E-05 19 0.003732163 19 5.41559E-0520 9.53674E-07 20 0.001866081 20 8.10005E-06