Let X ¼ Bin(n, p). a. Show that if x is an integer between 1 and n

Let X ˆ¼ Bin(n, p).

a. Show that if x is an integer between 1 and n inclusive, then

b. Show that if X ˆ¼ Bin(n, p), the most probable value for X is the greatest integer less than or equal to np + p. Use part (a) to show that P(X = x) ‰¥ P(X = x ˆ’ 1) if and only if x ‰¤ np + p.

Transcribed Image Text:

п — х +1 Р (X — х) 1- p Р(X — х — 1) х