For what values of $k$ is $f(x)$ a valid PMF

757 Views Asked by At

Im trying to solve this problem but I'm getting pretty confuse on how to approach the problem.

Let $X$ have the following PMF, where $k$ is a constant called a parameter

$$f(x) =\begin{cases} \cfrac {1-k}{2} & \text{when } x=-1,\\ k &\text{when } x=0,\\ \cfrac {1-k}{2} &\text{when }x=1. \end{cases}$$

Now do I find the values of $k$ for a valid PMF? I'm getting very lost and any help would be highly appreciated.

1

There are 1 best solutions below

1
On BEST ANSWER

Hint: to be a probability mass function, we must have (i) $\sum_{x} f(x) = 1$ and (ii) $f(x)\geq 0$ for all $x$.

(That's necessary, and sufficient.)