1A coin is tossed twice X is 1 if the first toss is heads an

1.A coin is tossed twice. X is 1 if the first toss is heads and 0 otherwise. Let Y equal the total number of heads. Give the joint probability distribution.

2.Find the joint probability distribution for the number of boys and girls in a family of three children.

Solution

1)

all possibile out comes are (X=1,Y=2) (X=1,Y=1) (X=0,Y=1) (X=0,Y=0)

since all the events are equally likely

so the joint distibution P(X,Y) = 1/4

2)

let X be the number of boys , let Y be the number of girls

the possilble outcomes are (X=0,Y=3) (X=1,Y=2) , (X=2,Y=1),(X=3 Y=0)

joint probability distribution P(X,Y) = 1/4