# Probability (probability mass function,pmf)

1. Dec 15, 2009

### naspek

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

2. Dec 15, 2009

### HallsofIvy

I think you mean "probability density function".

The total probability must be 1.
$\sum_{x=0}^\infty k/x!= k\sum_{x=0}^\infty 1/x!= 1$

Do you know what that sum is?

3. Dec 15, 2009

### naspek

i dont know.. is it infinity?

4. Dec 15, 2009

For discrete distributions these are usually called mass functions - density is reserved for continuous distributions.

naspek, HallsofIvy is asking whether you can identify what the sum

$$\sum_{x=0}^\infty \frac 1 {x!}$$

equals? This problem should remind you of a commonly used distribution.

5. Dec 15, 2009

### HallsofIvy

You probably have not taken calculus yet, but if you had you would have learned that
$$e^x= \sum_{n=0}^\infty \frac{x^n}{n!}$$.

Do you know what an "exponential probability distribution" is?

Last edited by a moderator: Dec 16, 2009
6. Dec 15, 2009

### naspek

ok.. now i understand already... thanks guys!! =)