what is the Pr(X=x)?
So this is an example straight from a book, like an example to help teach the material yet it makes absolutely no sense or I am just not seeing where they make the jump at.
We have the following: Consider the experiment consisting of 2 rolls of a fair 4-sided die. Let X be a random variable, equal to the maximum of the 2 rolls. It then says complete the following table (I don't know how to make a table on here)
| $\space$$\space$$\space$$\space$x$\space$$\space$$\space$$\space\,\,$ | 1 | 2 | 3 | 4 |
|Pr(X=x)| ? | ? | ? | ? |
With the sample space S ={(1, 1),(1, 2),(1, 3),(1, 4),(2, 1),(2, 2),(2, 3),(2, 4),(3, 1),(3, 2),(3, 3), (3, 4),(4, 1),(4, 2),(4, 3),(4, 4)}
I don't see how Pr(X=1) = $1\over16$, Pr(X=2) = $3\over16$, Pr(X=3) = $5\over16$ and Pr(X=4) = $7\over16$.
I can see that there is a total of seven 4's in the sample space but there's also seven 1's in the sample space, same with seven 2's and so on. Could anyone give a bit of a hint on what I'm missing? I've read the definitions and everything leading up to this example but they don't help.
$\endgroup$ 51 Answer
$\begingroup$For example, $X=3$ consists of the sample points $(1,3), (2,3), (3,1), (3,2), (3,3)$. There are $5$ of them, while the sample space has $16$ points, all equally probable, so $P(X=3) = 5/16$.
$\endgroup$ 3
