0.25
What value of $c$ makes the following a valid probability mass function? $$f(x) = \begin{cases} c, &x \in {1,2}\\ 2c, &x \in {5}\\ 0, &otherwise \end{cases}$$
0.25
From Thrm 1.2.9 we have the following:\[\sum_{x \in X(\Omega)} f(x) = 1\]
When we apply this to our specific equation we get the following:
\[\begin{align}1 &= \sum_{x \in 1,2,5} f(x)\\
&= f(1) + f(2) + f(5)\\
&= c + c + 2c\\
&= 4c\\
c &= 1/4 = 0.25\end{align}\]