Question

Flip a fair coin 100 times. Let X equal the number of heads in the first 65 flips. Let Y equal the number of heads in the remaining 35 flips.

(a) Find PX (x) and PY (y).
(b) In a couple of sentences, explain whether X and Y are or are not independent?

(c) Find PX,Y (x, y).

Answer 1

a)for ranfdom variable x is distributed binomially with paramter p=1/2 and n=65

therefore

P(x) =

similarly P(y) =

b) for number of heads in first 65 flips are number of heads in remaining 35 flips does not depend on each other therefore X and Y are independent.

c)due to independence:

P(x,y) =P(x)*P(y) =*