# Thread: [SOLVED] Probability (probability mass function,pmf)

1. ## [SOLVED] Probability (probability mass function,pmf)

If X has the probability mass function f(x) = k / x! (x=0,1,2,...),
what is the value of k?

2. Originally Posted by nameck
If X has the probability mass function f(x) = k / x! (x=0,1,2,...),
what is the value of k?
You must have $\sum_{x=0}^\infty \frac{k}{x!}= k\sum_{x=0}^\infty \frac{1}{x!}= 1$.

3. how to cancel the factorial(!) sign?

4. Originally Posted by nameck
how to cancel the factorial(!) sign?
At this level you are expected to know that $\sum\limits_{x = 0}^\infty {\frac{1}{{x!}}} = e$.