Define the random variable

Question

1. Consider the random variable X with the probability mass function p(i)=e^-22ⁱ/i!

What is P{X=0}?

2. Consider a fair coin. We define the random variable X=0 if the outcome is tail and X=1 if the outcome is head.

What is F_X(0)?  In other words, what is the CDF at X=0?

3. Consider a fair coin. We define the random variable X=0 if the outcome is tail and X=1 if the outcome is head.

What is F_X(1/2)?  In other words, what is the CDF at X=1/2?

4. Consider a fair coin. We define the random variable X=0 if the outcome is tail and X=1 if the outcome is head.

What is E[X]?