For what value of k px is a probability mass function I beli

For what value of k, p(x) is a probability mass function. I believe k > 0 to satisfy the first of the 3 required conditions, but I\'m not sure how to apply the others. Thanks in advance.

Solution

Note that a pmf must sum up to 1 for all values of x.

Here, we see that it is a geomtric series of first term a1 = k, and common ratio R = (1 - r^2).

For such, the sum is

Sum = a1 / (1 - R)

In this case,

Sum = k / (1 - (1 - r^2)) = k/r^2 = 1

Thus,

k/r^2 = 1

k = r^2 [ANSWER]