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The Binomial Distribution
1980.86
170.28170.28
29019.12
4.8825423.8392
Standard Deviation = 4.88254is the PDFis the (Cumulative) Distribution Function
x0 8.58E-170 8.58E-170 0 01 1.04E-166 1.04E-166 1.04E-166 1.04E-1662 6.31E-164 6.32E-164 1.26E-163 2.52E-1633 2.53E-161 2.54E-161 7.60E-161 2.28E-1604 7.59E-159 7.61E-159 3.03E-158 1.21E-1575 1.81E-156 1.82E-156 9.04E-156 4.52E-1556 3.57E-154 3.59E-154 2.14E-153 1.29E-1527 6.02E-152 6.06E-152 4.21E-151 2.95E-1508 8.83E-150 8.89E-150 7.06E-149 5.65E-1489 1.14E-147 1.15E-147 1.03E-146 9.27E-14610 1.33E-145 1.34E-145 1.33E-144 1.33E-14311 1.40E-143 1.41E-143 1.54E-142 1.69E-14112 1.34E-141 1.35E-141 1.60E-140 1.92E-13913 1.17E-139 1.19E-139 1.53E-138 1.98E-13714 9.53E-138 9.65E-138 1.33E-136 1.87E-13515 7.18E-136 7.28E-136 1.08E-134 1.62E-13316 5.05E-134 5.12E-134 8.07E-133 1.29E-13117 3.32E-132 3.37E-132 5.64E-131 9.59E-13018 2.05E-130 2.08E-130 3.69E-129 6.64E-12819 1.19E-128 1.21E-128 2.27E-127 4.31E-12620 6.56E-127 6.68E-127 1.31E-125 2.62E-12421 3.41E-125 3.48E-125 7.17E-124 1.51E-12222 1.69E-123 1.72E-123 3.71E-122 8.17E-12123 7.93E-122 8.11E-122 1.82E-120 4.20E-11924 3.55E-120 3.63E-120 8.53E-119 2.05E-11725 1.52E-118 1.56E-118 3.80E-117 9.50E-11626 6.21E-117 6.37E-117 1.61E-115 4.20E-11427 2.43E-115 2.49E-115 6.56E-114 1.77E-11228 9.12E-114 9.37E-114 2.55E-112 7.15E-11129 3.28E-112 3.38E-112 9.52E-111 2.76E-10930 1.14E-110 1.17E-110 3.41E-109 1.02E-107
n =p =< x > = mean = np =Sum of x*b(x) =
< x2 > = Sum of x2*b(x) =
< x2 > - <x>2 =Variance = np(1 - p)
b(x)B(x)
b(x) B(x) x*b(x) x2*b(x)
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09Binomial Distribution
31 3.78E-109 3.90E-109 1.17E-107 3.63E-10632 1.21E-107 1.25E-107 3.88E-106 1.24E-10433 3.75E-106 3.87E-106 1.24E-104 4.08E-10334 1.12E-104 1.16E-104 3.80E-103 1.29E-10135 3.21E-103 3.33E-103 1.13E-101 3.94E-10036 8.94E-102 9.27E-102 3.22E-100 1.16E-09837 2.40E-100 2.50E-100 8.90E-099 3.29E-09738 6.26E-099 6.51E-099 2.38E-097 9.04E-09639 1.58E-097 1.64E-097 6.15E-096 2.40E-09440 3.85E-096 4.02E-096 1.54E-094 6.16E-09341 9.12E-095 9.52E-095 3.74E-093 1.53E-09142 2.09E-093 2.19E-093 8.79E-092 3.69E-09043 4.67E-092 4.88E-092 2.01E-090 8.63E-08944 1.01E-090 1.06E-090 4.44E-089 1.95E-08745 2.12E-089 2.23E-089 9.55E-088 4.30E-08646 4.34E-088 4.56E-088 1.99E-086 9.18E-08547 8.61E-087 9.07E-087 4.05E-085 1.90E-08348 1.66E-085 1.76E-085 7.99E-084 3.84E-08249 3.13E-084 3.31E-084 1.53E-082 7.52E-08150 5.73E-083 6.06E-083 2.87E-081 1.43E-07951 1.02E-081 1.08E-081 5.21E-080 2.66E-07852 1.77E-080 1.88E-080 9.22E-079 4.80E-07753 3.00E-079 3.19E-079 1.59E-077 8.43E-07654 4.95E-078 5.27E-078 2.67E-076 1.44E-07455 7.96E-077 8.49E-077 4.38E-075 2.41E-07356 1.25E-075 1.33E-075 7.00E-074 3.92E-07257 1.91E-074 2.05E-074 1.09E-072 6.21E-07158 2.85E-073 3.06E-073 1.66E-071 9.60E-07059 4.16E-072 4.47E-072 2.46E-070 1.45E-06860 5.92E-071 6.37E-071 3.55E-069 2.13E-06761 8.23E-070 8.87E-070 5.02E-068 3.06E-06662 1.12E-068 1.21E-068 6.93E-067 4.29E-06563 1.48E-067 1.60E-067 9.33E-066 5.88E-06464 1.92E-066 2.08E-066 1.23E-064 7.86E-06365 2.43E-065 2.64E-065 1.58E-063 1.03E-06166 3.01E-064 3.27E-064 1.99E-062 1.31E-06067 3.64E-063 3.97E-063 2.44E-061 1.63E-05968 4.31E-062 4.71E-062 2.93E-060 1.99E-05869 4.99E-061 5.46E-061 3.44E-059 2.37E-05770 5.65E-060 6.19E-060 3.95E-058 2.77E-05671 6.25E-059 6.87E-059 4.44E-057 3.15E-05572 6.77E-058 7.46E-058 4.88E-056 3.51E-05473 7.18E-057 7.93E-057 5.24E-055 3.83E-05374 7.45E-056 8.25E-056 5.52E-054 4.08E-05275 7.57E-055 8.39E-055 5.68E-053 4.26E-051
76 7.53E-054 8.37E-054 5.72E-052 4.35E-05077 7.32E-053 8.16E-053 5.64E-051 4.34E-04978 6.98E-052 7.80E-052 5.44E-050 4.25E-04879 6.51E-051 7.29E-051 5.15E-049 4.06E-04780 5.95E-050 6.68E-050 4.76E-048 3.81E-04681 5.33E-049 5.99E-049 4.31E-047 3.49E-04582 4.67E-048 5.27E-048 3.83E-046 3.14E-04483 4.01E-047 4.53E-047 3.33E-045 2.76E-04384 3.37E-046 3.82E-046 2.83E-044 2.38E-04285 2.78E-045 3.16E-045 2.36E-043 2.01E-04186 2.24E-044 2.56E-044 1.93E-042 1.66E-04087 1.77E-043 2.03E-043 1.54E-041 1.34E-03988 1.37E-042 1.58E-042 1.21E-040 1.06E-03889 1.04E-041 1.20E-041 9.28E-040 8.26E-03890 7.76E-041 8.96E-041 6.98E-039 6.28E-03791 5.65E-040 6.55E-040 5.15E-038 4.68E-03692 4.04E-039 4.70E-039 3.72E-037 3.42E-03593 2.83E-038 3.30E-038 2.63E-036 2.45E-03494 1.94E-037 2.27E-037 1.82E-035 1.71E-03395 1.31E-036 1.53E-036 1.24E-034 1.18E-03296 8.60E-036 1.01E-035 8.26E-034 7.93E-03297 5.56E-035 6.57E-035 5.39E-033 5.23E-03198 3.52E-034 4.17E-034 3.45E-032 3.38E-03099 2.18E-033 2.60E-033 2.16E-031 2.14E-029
100 1.33E-032 1.59E-032 1.33E-030 1.33E-028101 7.91E-032 9.50E-032 7.99E-030 8.07E-028102 4.62E-031 5.57E-031 4.71E-029 4.81E-027103 2.65E-030 3.20E-030 2.73E-028 2.81E-026104 1.48E-029 1.81E-029 1.54E-027 1.61E-025105 8.17E-029 9.97E-029 8.57E-027 9.00E-025106 4.40E-028 5.40E-028 4.67E-026 4.95E-024107 2.32E-027 2.86E-027 2.49E-025 2.66E-023108 1.20E-026 1.49E-026 1.30E-024 1.40E-022109 6.10E-026 7.59E-026 6.65E-024 7.25E-022110 3.03E-025 3.79E-025 3.34E-023 3.67E-021111 1.48E-024 1.86E-024 1.64E-022 1.82E-020112 7.05E-024 8.90E-024 7.89E-022 8.84E-020113 3.30E-023 4.19E-023 3.72E-021 4.21E-019114 1.51E-022 1.93E-022 1.72E-020 1.96E-018115 6.77E-022 8.70E-022 7.79E-020 8.96E-018116 2.98E-021 3.85E-021 3.45E-019 4.01E-017117 1.28E-020 1.67E-020 1.50E-018 1.75E-016118 5.40E-020 7.07E-020 6.38E-018 7.52E-016119 2.23E-019 2.94E-019 2.66E-017 3.16E-015120 9.02E-019 1.20E-018 1.08E-016 1.30E-014
121 3.57E-018 4.77E-018 4.32E-016 5.23E-014122 1.39E-017 1.86E-017 1.69E-015 2.06E-013123 5.26E-017 7.12E-017 6.47E-015 7.96E-013124 1.95E-016 2.67E-016 2.42E-014 3.00E-012125 7.10E-016 9.77E-016 8.88E-014 1.11E-011126 2.53E-015 3.51E-015 3.19E-013 4.01E-011127 8.81E-015 1.23E-014 1.12E-012 1.42E-010128 3.00E-014 4.23E-014 3.84E-012 4.92E-010129 1.00E-013 1.42E-013 1.29E-011 1.66E-009130 3.26E-013 4.68E-013 4.24E-011 5.51E-009131 1.04E-012 1.51E-012 1.36E-010 1.78E-008132 3.24E-012 4.75E-012 4.28E-010 5.65E-008133 9.88E-012 1.46E-011 1.31E-009 1.75E-007134 2.94E-011 4.41E-011 3.95E-009 5.29E-007135 8.58E-011 1.30E-010 1.16E-008 1.56E-006136 2.44E-010 3.74E-010 3.32E-008 4.51E-006137 6.78E-010 1.05E-009 9.29E-008 1.27E-005138 1.84E-009 2.89E-009 2.54E-007 3.51E-005139 4.88E-009 7.78E-009 6.79E-007 9.44E-005140 1.26E-008 2.04E-008 1.77E-006 0.000248141 3.20E-008 5.24E-008 4.51E-006 0.000635142 7.88E-008 1.31E-007 1.12E-005 0.001589143 1.90E-007 3.21E-007 2.71E-005 0.003876144 4.45E-007 7.65E-007 6.40E-005 0.009221145 1.02E-006 1.78E-006 0.000148 0.021389146 2.27E-006 4.05E-006 0.000331 0.048357147 4.93E-006 8.98E-006 0.000725 0.106523148 1.04E-005 1.94E-005 0.001544 0.228566149 2.15E-005 4.09E-005 0.003205 0.477545150 4.32E-005 8.41E-005 0.006475 0.971179151 8.43E-005 0.000168 0.012727 1.921788152 0.00016 0.000328 0.024334 3.698821153 0.000296 0.000624 0.045238 6.92143154 0.000531 0.001155 0.081733 12.58684155 0.000925 0.00208 0.143449 22.23463156 0.001567 0.003647 0.244459 38.13555157 0.002575 0.006223 0.404297 63.47463158 0.004105 0.010327 0.648567 102.4737159 0.006344 0.016671 1.008622 160.3709160 0.009498 0.026169 1.51973 243.1568161 0.013771 0.039941 2.217177 356.9655162 0.019321 0.059262 3.130017 507.0627163 0.026213 0.085475 4.272722 696.4536164 0.034365 0.119839 5.635798 924.2709165 0.043499 0.163338 7.177297 1184.254
166 0.053119 0.216457 8.817822 1463.758167 0.062526 0.278983 10.44176 1743.774168 0.070873 0.349856 11.90664 2000.316169 0.077283 0.427139 13.06086 2207.285170 0.080985 0.508124 13.76745 2340.466171 0.081459 0.589583 13.92942 2381.93172 0.078549 0.668132 13.51049 2323.804173 0.072517 0.740649 12.54545 2170.363174 0.064003 0.804652 11.13655 1937.759175 0.053919 0.858571 9.435893 1651.281176 0.043284 0.901856 7.61804 1340.775177 0.033048 0.934904 5.849566 1035.373178 0.023951 0.958855 4.263243 758.8573179 0.016439 0.975294 2.942527 526.7124180 0.010659 0.985953 1.918631 345.3536181 0.006512 0.992464 1.178588 213.3244182 0.003736 0.996201 0.67999 123.7582183 0.002007 0.998207 0.367216 67.20054184 0.001005 0.999212 0.184898 34.02124185 0.000467 0.999679 0.08642 15.98765186 0.000201 0.99988 0.037304 6.938537187 7.91E-005 0.999959 0.014784 2.764619188 2.84E-005 0.999987 0.005342 1.004322189 9.24E-006 0.999996 0.001746 0.329905190 2.69E-006 0.999999 0.000511 0.097014191 6.91E-007 1 0.000132 0.025224192 1.55E-007 1 2.97E-005 0.005708193 2.96E-008 1 5.71E-006 0.001102194 4.68E-009 1 9.08E-007 0.000176195 5.90E-010 1 1.15E-007 2.24E-005196 5.55E-011 1 1.09E-008 2.13E-006197 3.46E-012 1 6.81E-010 1.34E-007198 1.07E-013 1 2.12E-011 4.21E-009199 0 1 0 0200 0 1 0 0201 0 1 0 0202 0 1 0 0203 0 1 0 0204 0 1 0 0205 0 1 0 0206 0 1 0 0207 0 1 0 0208 0 1 0 0209 0 1 0 0210 0 1 0 0
211 0 1 0 0212 0 1 0 0213 0 1 0 0214 0 1 0 0215 0 1 0 0216 0 1 0 0217 0 1 0 0218 0 1 0 0219 0 1 0 0220 0 1 0 0221 0 1 0 0222 0 1 0 0223 0 1 0 0224 0 1 0 0225 0 1 0 0226 0 1 0 0227 0 1 0 0228 0 1 0 0229 0 1 0 0230 0 1 0 0231 0 1 0 0232 0 1 0 0233 0 1 0 0234 0 1 0 0235 0 1 0 0236 0 1 0 0237 0 1 0 0238 0 1 0 0239 0 1 0 0240 0 1 0 0241 0 1 0 0242 0 1 0 0243 0 1 0 0
1
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09Binomial Distribution
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09Binomial Distribution
