Easy distributions for combinatorial optimization problems with probabilistic constraints

We show how we can linearize individual probabilistic linear constraints with binary variables when all coefficients are independently distributed according to either N(μi,λμi)N(μi,λμi), for some λ>0λ>0 and μi>0μi>0, or Γ(ki,θ)Γ(ki,θ) for some θ>0θ>0 and ki>0ki>0. The constraint can also be linearized when the coefficients are independent and identically distributed and either positive or strictly stable random variables.