Probability Distribution of Random Variable X from a Double Dice Roll Experiment

[ampakine]

The question is "An experiment in which a dice is tossed twice. Let X be the random variable defined by recording the higher of the 2 values obtained in the experiment. Determine the probability distribution of X."

I know that the range of this distribution is {1,2,3,4,5,6}. For P(X=1) both rolls will have to land on 1 so the probability is 1/36. As for P(X=2) I assumed that 1 dice has to land on 2 so that has a 1/6 probability and the other can land on either 1 or 2 so that's a 2/6 probability. Multiplying them together I get 2/36 but according to the answer I have for this question that's wrong. Heres the real answer:
http://imageshack.us/m/535/4747/distk.png
What am I doing wrong?

 

[tiny-tim]

hi ampakine!

As for P(X=2) I assumed that 1 dice has to land on 2 so that has a 1/6 probability and the other can land on either 1 or 2 so that's a 2/6 probability. Multiplying them together I get 2/36 …

no, because your method assumes that the first number is higher (if they're not equal)

either number can be higher

in other words: you've counted (2,1) and (2,2) but not (1,2)

 

[ampakine]

Ah right, that explains it. Thanks a lot!

 

[bpet]

An easier way to derive the probability of maximums (and works with both discrete and cts distributions) is to first find the cdf:

P[max(X,Y)<=x] = P[X<=x,Y<=x] = P[X<=x]^2

then take the differences or derivatives to get the pmf or pdf.