Let \(X\) be a random variable with probability mass function

\[p(n) = \frac{c}{n!}\quad \text{for $\mathbf{N}=0,1,2\cdots$}\]

and \(p(x)=0\) otherwise.

1. Find \(c\). Hint use the Taylor series expansion of \(e^x\).
2. Compute the probability that \(X\) is even.
3. Computer the expected value of \(X\)

[Meester ex 2.7.14]