Question

Three cards are randomly chosen, without replacement, from a standard deck of
52. The random variable X represents the number of hearts cards chosen.
Construct the probability distribution for X.

Answer 1

Sample space, S={0,1,2,3}

PDF:
-∞<X<0 P(X)=0
P(0)=39*38*37/3! /C(52,3) no heart
P(1)=13*39*38/2! /C(52,3) 1 heart, 2 cards of other suits
P(2)=13*12/2!*39 /C(52,3) 2 hearts, 1 card of other suits
P(3)=13*12*11/3! /C(52,3) 3 hearts
3<X<∞ P(X)=0

Make sure that the values of the discrete PDF add up to 1.