Prove Theorem 5 5 13 that is, show that a Set e x and show that if x , then P(Xn x) P( Xn ) Deduce the implication b Use the fact that x x x x to deduce the (See Billingsley 1995, Section 25, for a detailed treatment of the above results ) 0 if...

a Let x i For x 0 PX n PX n x PX n x PX n x PX n x PX n x 1 PX n x Therefore 0 limn PX n ...

Prove Theorem 5.5.13; that is, show that a. Set e = |x - | and show that

Question:

Prove Theorem 5.5.13; that is, show that

a. Set e = |x - Î¼| and show that if x > Î¼, then P(Xn ‰¤ x) > P(|Xn - Î¼| ˆˆ). Deduce the => implication.
b. Use the fact that {x : |x - Î¼ >ˆˆ} = {x : x - Î¼. ˆˆ} to deduce the (See Billingsley 1995, Section 25, for a detailed treatment of the above results.)