Probability Mass Function Question

Hi, I'm new to this forum, and I was wondering if I could get some help with probability. Could someone explain to me (if possible) how do you go about finding a probability mass function (pmf)?

Here is the exact question:
Let a random experiment be the cast of a pair of unbiased six-sided dice and let X equal the smaller of the outcomes if they are different and the common value if they are equal. With reasonable assumptions, find the pmf of X.

Any help would be greatly appreciated. Thanks!!!

Reply 1

Jonny W

Write the value of X for each of the 36 possible outcomes in a table.

...1 2 3 4 5 6
1 1 1 1 1 1 1
2 1 2 2 2 2 2
3 1 2 3 3 3 3
4 1 2 3 4 4 4
5 1 2 3 4 5 5
6 1 2 3 4 5 6

Since each outcome occurs with probability 1/36,

f(x) = (number of times x appears in the table)/36

f(1) = 11/36
f(2) = 9/36
f(3) = 7/36
f(4) = 5/36
f(5) = 3/36
f(6) = 1/36

Reply 2

40wada

Thanks, I understand that part. I'm sorry I didn't post the answer earlier, but the answer is f(x)=(13-2x)/36. I guess I understand why the answer has a 36 in the denominator, but I don't understand how the numerator is (13-2x). Well, I understand why it is (13-2x), but I just don't understand how they came up with that answer or how to solve for it. If you know how to explain this to me, I would greatly appreciate it. Thanks!!!

Reply 3

Jonny W

Looking at

f(1) = 11/36
f(2) = 9/36
f(3) = 7/36
f(4) = 5/36
f(5) = 3/36
f(6) = 1/36

you can see that the numerator goes down by 2 between each pair of successive lines. So f(x) = (A - 2x)/36 for some constant A. Since f(1) = 11/36, A - 2 = 11 and A = 13. So f(x) = (13 - 2x)/36.