Question

Suppose that two fair dice are rolled and that the two
numbers recorded are multiplied to obtain a final score.
Construct and plot the probability mass function and the
cumulative distribution function of the final score

Answer 1

make a six by six multiplication table as a first step

Answer 2

alright. I got the probabilities of thm.

Answer 3

then each entry will have probability \(\frac{1}{36}\) add them up to get the probability of each outcome
for example, \(P(x=12)=\frac{4}{36}=\frac{1}{9}\) because there are 4 ways to get a 12: \(\{(2,6),(6,2),(3,4),(4,3)\}\)

Answer 4

So the probability of getting, say, 6 is P(6)=4/36. Thats how you would get the answers for pmf? Then to find cdf, you add up the pdf probabilities?

Answer 5

ok then that is all a probability mass function is
if your random variable is called \(X\) then in this case \(X\) takes on possible values : 1,2,3,4,5,6,8,9,10,12,15,16,18,20,25,30,36
find the probability of each one
\[P(X=12)=\frac{1}{9}\] for example
the complete answer is the probability mass function

Answer 6

yes to your second question
for example \(F_X(1)=\frac{1}{36}\) and \(F_X(2)=\frac{3}{36}\)

Answer 7

will the denominator of each P9X) be 36?

Answer 8

the mass function is sometimes written as
\(f_X(x)\) instead of \(P(X=x)\) but they mean the same thing
so in your example you have as you said \(f_X(6)=4\)

Answer 9

oops i meant
\[f_X(6)=\frac{4}{36}\] sorry

Answer 10

ok. and the cdf of 36 has to be 1?

Answer 11

and yes, the denominators will all be 36
i would not reduce the fraction because for the second part you have to add, so leave the denominators as 36

Answer 12

the total will be one, yes
i.e. \(F_X(36)=1\)

Answer 13

So after I construct the 6x6 matrix, and the table consisting of X, P(X), and cdf, is that all?

Answer 14

yes, that is all it asks

Answer 15

HA! Thank you SO VERY MUCH!

Answer 16

yw

Answer 17

What do you do for a living? Just a question