Prove a special case of Theorem 9 3 2 Let X f x), where is a symmetric unimodal pdf For a fixed value of 1 , of all intervals a, b that satisfy ba f(x)dx 1 , the shortest is obtained by choosing a and b so that a f(x) dx a 2 and b f(x) dx 2 ...

Let a be such that a f x dx 2 This value is unique for a unimodal pdf ...

Prove a special case of Theorem 9.3.2. Let X ~ f{x), where / is a symmetric unimodal

Question:

Prove a special case of Theorem 9.3.2. Let X ~ f{x), where / is a symmetric unimodal pdf. For a fixed value of 1 - α, of all intervals [a, b] that satisfy ∫ba f(x)dx= 1 - α, the shortest is obtained by choosing a and b so that ∫a-∞ f(x) dx = a/2 and ∫∞b f(x) dx = α/2.