By use of the definition of the beta functionB(p, q) \equiv \in... | Filo

Beta Distribution | Definition & Examples

SOLVED:The Beta function, which is important in many branches of mathematics, is defined as B(α, β)=∫0^1 x^α-1(1-x)^β-1 d x with the condition that α≥1 and β≥1. (a) Show by a change of variables that B(α, β)=∫0^1 x^β-1(1-x)^α-1 d x=B(β, α) (b) Integrate by parts to show that B(α, β)=(α-1)/(β) B(α-1, β 1)=(β-1)/(α) B(α 1, β-1) (c) Assume now that α=n and β=m, and that n and m are positive integers. By using the result in part (b) repeatedly, show that B(n, m)=((n-1) !(m-1) !)/((n m-1) !) This res

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