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Using a Mass Function
Let \(X\) be a random variable with probability mass function
\(p(n) = \frac{1}{c^n}\quad \text{for } n=2,3,4,\cdots\)
and \(p(x)=0\) otherwise.
- Find \(c.\)
- Compute the probability that \(X\) is even.
A p.m.f. and expectation example
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.
- Find \(c\). Hint use the Taylor series expansion of \(e^x\).
- Compute the probability that \(X\) is even.
- Computer the expected value of \(X\)
[Meester ex 2.7.14]
