Let \(X\) be a random variable with the following pmf:

\(x\) \(P(X=x)\)
-1 0.500
0 0.250
1 0.125
2 0.125
  1. What is the mean of \(X\)?
  2. What is the pmf of \(Y = 2X-3\)?
  3. What is the mean of \(Y\)?
  4. What is the pmf of \(W = X^2\)?
  5. What is the mean of \(W\)?
  6. What is the conditional pmf of \(X\) given \(X \neq 0\)?
  7. What is the conditional mean of \(X\) given \(X \neq 0\)?