1. ## PmF

A fair coin is tossed four times, and the random variable X is the number of heads in the first three tosses and the random variable Y is the number of heads in the last three tosses.

Find the joint probability mass function and marginal probability mass function of X and Y.

ON this problem, I did HHHH, HHHT, HHTH,....and so on. Is that how you start off and make a table from there. like there is a 1/13 chance of getting first three heads? I am not completely sure.

2. Originally Posted by durham2
A fair coin is tossed four times, and the random variable X is the number of heads in the first three tosses and the random variable Y is the number of heads in the last three tosses.

Find the joint probability mass function and marginal probability mass function of X and Y.

ON this problem, I did HHHH, HHHT, HHTH,....and so on. Is that how you start off and make a table from there. like there is a 1/13 chance of getting first three heads? I am not completely sure.
List all the outcomes and use these to set up a table with X along the top and Y along the side. By the way, probability that the first three are heads is Pr(HHHT) + Pr(HHHH) = 1/16 + 1/16 = 1/8 ....

3. Originally Posted by mr fantastic
List all the outcomes and use these to set up a table with X along the top and Y along the side. By the way, probability that the first three are heads is Pr(HHHT) + Pr(HHHH) = 1/16 + 1/16 = 1/8 ....

okk so you put all 16 outcomes in a table? or is it 0-4 for how many heads you can get?

4. Originally Posted by durham2
okk so you put all 16 outcomes in a table? or is it 0-4 for how many heads you can get?
If
X is the number of heads in the first three tosses
then what is the minimum and maximum possible value of X?

If
the random variable Y is the number of heads in the last three tosses
then what is the minimum and maximum possible value of Y?

5. Originally Posted by durham2
okk so you put all 16 outcomes in a table? or is it 0-4 for how many heads you can get?
For X,Y seperately 0-3 might be sufficient.