Originally Posted by

**gconfused** An unbiased coin is tossed three times. Let X be the number of heads on the first toss and Y the number of heads on the second and third tosses combined. Find the joint density function of X and Y.

Hmm i reckon I'm wrong but is the correct answer 1/2? Mr F says: Answer to what?? The joint density function is the table you drew below (which is correct, by the way). I don't see any other question in your post ....?

SOrry i don't know how to draw a table here but all i did for this question was add up the row total??

so 1/8 + 1/4 + 1/8

_______Y________

_______0________1_________2__

0 |....1/8...1/4....1/8

1 |....1/8...1/4...1/8 | X

P(X = 0, Y=0) = 1/8

P(X=0, Y=1) = 1/4

P(X=0,Y=2) = 1/8

which equals to 1/2... is this what I'm supposed to do or am i way off(highly likely)?

Yeahhh and here are the possibilities i drew up:

______X Y__

HHH 1 2

HHT 1 1

HTH 1 1

THH 0 2

HTT 1 0

THT 0 1

TTH 0 1

TTT 0 0