SM-4-ProbabilityGeneratingFunction

4136 days ago by MathFest

expand((.2*x+.3*x^2+.25*x^3+.05*x^4+.1*x^5+.1*x^6)*(.02*x^2+.03*x^3+.02*x^4+.03*x^5+.9*x^6)*(.1*x+.15*x^2+.25*x^3+.25*x^4+.15*x^5+.1*x^6)*(.4*x+.05*x^2+.05*x^3+.05*x^4+.05*x^5+.4*x^6)) 
       
0.00360000000000000*x^24 + 0.00957000000000000*x^23 +
0.0181700000000000*x^22 + 0.0342225000000000*x^21 +
0.0524125000000000*x^20 + 0.0784887500000000*x^19 +
0.0992987500000000*x^18 + 0.108597500000000*x^17 +
0.110690000000000*x^16 + 0.103937500000000*x^15 + 0.101407500000000*x^14
+ 0.0938725000000000*x^13 + 0.0794575000000000*x^12 +
0.0560537500000000*x^11 + 0.0303837500000000*x^10 +
0.0131475000000000*x^9 + 0.00384000000000000*x^8 +
0.00195000000000000*x^7 + 0.000740000000000000*x^6 +
0.000160000000000000*x^5
0.00360000000000000*x^24 + 0.00957000000000000*x^23 + 0.0181700000000000*x^22 + 0.0342225000000000*x^21 + 0.0524125000000000*x^20 + 0.0784887500000000*x^19 + 0.0992987500000000*x^18 + 0.108597500000000*x^17 + 0.110690000000000*x^16 + 0.103937500000000*x^15 + 0.101407500000000*x^14 + 0.0938725000000000*x^13 + 0.0794575000000000*x^12 + 0.0560537500000000*x^11 + 0.0303837500000000*x^10 + 0.0131475000000000*x^9 + 0.00384000000000000*x^8 + 0.00195000000000000*x^7 + 0.000740000000000000*x^6 + 0.000160000000000000*x^5
f(x)=(.2*x+.3*x^2+.25*x^3+.05*x^4+.1*x^5+.1*x^6)*(.02*x^2+.03*x^3+.02*x^4+.03*x^5+.9*x^6)*(.1*x+.15*x^2+.25*x^3+.25*x^4+.15*x^5+.1*x^8)*(.4*x+.05*x^2+.05*x^3+.05*x^4+.05*x^5+.4*x^6) f(1) 
       
1.00000000000000
1.00000000000000
f(x)=(.2*x+.3*x^2+.25*x^3+.05*x^4+.1*x^5+.1*x^6)*(.02*x^2+.03*x^3+.02*x^4+.03*x^5+.9*x^6)*(.1*x+.15*x^2+.25*x^3+.25*x^4+.15*x^5+.1*x^8)*(.4*x+.05*x^2+.05*x^3+.05*x^4+.05*x^5+.4*x^6) g(x)=derivative(f(x),x) g(1) 
       
15.8100000000000
15.8100000000000
f(x)=(.2*x+.3*x^2+.25*x^3+.05*x^4+.1*x^5+.1*x^6)*(.02*x^2+.03*x^3+.02*x^4+.03*x^5+.9*x^6)*(.1*x+.15*x^2+.25*x^3+.25*x^4+.15*x^5+.1*x^8)*(.4*x+.05*x^2+.05*x^3+.05*x^4+.05*x^5+.4*x^6) g(x)=derivative(f(x),x) h(x)=derivative(g(x),x) h(1)+g(1)-(g(1))^2 
       
11.7299000000000
11.7299000000000