Page 1 Probability as a modeling tool for prediction e.g., â€¢ gaming odds â€¢ part construction â€¢ inventory modeling Probability Distributions Page 2 Probability as a modeling tool for prediction e.g., â€¢ gaming odds â€¢ part construction â€¢ inventory modeling Probability Distributions Probability as a modeling tool for prediction e.g., â€¢ gaming odds â€¢ part construction â€¢ inventory modeling Objective Objective: derive a function (pdf/pmf) that can be used to accurately predict outcomes of an experiment. Probability Distributions Page 3 Probability as a modeling tool for prediction e.g., â€¢ gaming odds â€¢ part construction â€¢ inventory modeling Probability Distributions Probability as a modeling tool for prediction e.g., â€¢ gaming odds â€¢ part construction â€¢ inventory modeling Objective Objective: derive a function (pdf/pmf) that can be used to accurately predict outcomes of an experiment. Probability Distributions So farâ€¦ f f ( (x x) ) = 1.5 = 1.5 â€“ â€“ 6( 6(x x - - 50) 50) 2 2 49.5 49.5 ? ? x x ? ? 50.5 50.5 40 / 40 1 x e f(x) ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 3 0 14 8 3 0 2 64 64 15 x x x x f(x) â€¢ â€¢ â€¢ â€¦ etc 0 ? x Probability Distributions Page 4 Probability as a modeling tool for prediction e.g., â€¢ gaming odds â€¢ part construction â€¢ inventory modeling Probability Distributions Probability as a modeling tool for prediction e.g., â€¢ gaming odds â€¢ part construction â€¢ inventory modeling Objective Objective: derive a function (pdf/pmf) that can be used to accurately predict outcomes of an experiment. Probability Distributions So farâ€¦ f f ( (x x) ) = 1.5 = 1.5 â€“ â€“ 6( 6(x x - - 50) 50) 2 2 49.5 49.5 ? ? x x ? ? 50.5 50.5 40 / 40 1 x e f(x) ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 3 0 14 8 3 0 2 64 64 15 x x x x f(x) â€¢ â€¢ â€¢ â€¦ etc 0 ? x Probability Distributions â€¢ Exponential â€¢ Gamma â€¢ Normal â€¢ Uniform â€¢ Bernoulli â€¢ Binomial â€¢ Geometric â€¢ Negative binomial Special Distributions Discrete Continuous Page 5 Probability as a modeling tool for prediction e.g., â€¢ gaming odds â€¢ part construction â€¢ inventory modeling Probability Distributions Probability as a modeling tool for prediction e.g., â€¢ gaming odds â€¢ part construction â€¢ inventory modeling Objective Objective: derive a function (pdf/pmf) that can be used to accurately predict outcomes of an experiment. Probability Distributions So farâ€¦ f f ( (x x) ) = 1.5 = 1.5 â€“ â€“ 6( 6(x x - - 50) 50) 2 2 49.5 49.5 ? ? x x ? ? 50.5 50.5 40 / 40 1 x e f(x) ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 3 0 14 8 3 0 2 64 64 15 x x x x f(x) â€¢ â€¢ â€¢ â€¦ etc 0 ? x Probability Distributions â€¢ Exponential â€¢ Gamma â€¢ Normal â€¢ Uniform â€¢ Bernoulli â€¢ Binomial â€¢ Geometric â€¢ Negative binomial Special Distributions Discrete Continuous The simplest random variable: either 1 or 0 either 1 or 0 Bernoulli DistributionRead More