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**Glitch** The question:

$\displaystyle p(X = k) = \frac{c}{k!}$, k = 0, 1, 2, ...

a) Determine the value of c.

b) Calculate $\displaystyle P(X = 2)$

c) Calculate $\displaystyle P(X < 2)$

d) Calculate $\displaystyle P(X \ge 4)$

I think I know how to do b), c) and d), but a) is giving me trouble.

I tried this:

$\displaystyle \sum\limits_{i = 0}^{k} \frac{c}{i!} = 1$ (since it's a distribution)

$\displaystyle \sum\limits_{i = 0}^{k} \frac{1}{i!} = \frac{1}{c}$

I'm confident I've done this completely wrong. Any advice?