0.1000000000001 0.1000000000001 0.1000000000001 0.1000000000001 0.1000000000001 0.1000000000001 0.1000000000001 0.1000000000001 0.1000000000000998 0.09999999999910014 0.1000000000001 0.1000000000001 0.1000000000001 0.1000000000001 0.1000000000001 0.1000000000001 0.1000000000001 0.1000000000001 0.1000000000000998 0.09999999999910014 Distribution_Two_Sigma Distribution_Two_Beta Distribution_Two=Beta(Choose(Distribution_Two_Sigma,1000,100,50,10,5,4,3,2,1,0.5),Choose(Distribution_Two_Beta,1000,100,50,10,5,4,3,2,1,0.5)) 0.1000000000001 0.1000000000001 0.1000000000001 0.1000000000001 0.1000000000001 0.1000000000001 0.1000000000001 0.1000000000001 0.1000000000000998 0.09999999999910014 0.1000000000001 0.1000000000001 0.1000000000001 0.1000000000001 0.1000000000001 0.1000000000001 0.1000000000001 0.1000000000001 0.1000000000000998 0.09999999999910014 Distribution_One_Sigma Distribution_One_Beta Distribution_One=Beta(Choose(Distribution_One_Sigma,1000,100,50,10,5,4,3,2,1,0.5),Choose(Distribution_One_Beta,1000,100,50,10,5,4,3,2,1,0.5)) Distribution_One Distribution_Two Combined_Distribution_Multiplied=Distribution_One*Distribution_Two Distribution_One_Sigma Distribution_One_Beta Distribution_Two_Sigma Distribution_Two_Beta Combined_Distribution_Parameterized=Beta(Choose(Distribution_One_Sigma,1000,100,50,10,5,4,3,2,1,0.5)+Choose(Distribution_Two_Sigma,1000,100,50,10,5,4,3,2,1,0.5),Choose(Distribution_One_Beta,1000,100,50,10,5,4,3,2,1,0.5)+Choose(Distribution_Two_Beta,1000,100,50,10,5,4,3,2,1,0.5)) 0.5 0.5 Distribution_One Distribution_Two Proportion Mixture=Choose(Proportion,Distribution_One,Distribution_Two) Distribution Two 636 383 697 421 Sigma 530 613 576 641 Beta 755 613 801 641 Distribution One 201 383 262 421 Sigma 95 613 141 641 Beta 305 613 351 641 Combined Distribution (Multiplied) 272 125 333 163 Combined Distribution (Parameterized) 697 105 758 143 Proportion 1066 551 1128 589 Mixture 1118 205 1179 243