13. Prove the following identities: (a) As in (10.65): s2 EX2 EX2. (b) As in...

13. Prove the following identities:

(a) As in (10.65): s2 ¼ E½X2  E½X2.

(b) As in (10.66):

i. mn ¼

Pn j¼0ð1Þnj n j



m0jmnj (Hint: Use the binomial theorem.)

ii. m0n

¼

Pn j¼0 n

j



mjmnj (Hint: X ¼ ½X  m þ m.)