\begin{tabular}{|l|l|l|l|l|}
\hline \( \mathbf{X} \) & \( \mathbf{- 1} \) & \( \mathbf{0} \) & \( \mathbf{1} \) & \( \mathbf{4} \) \\
\hline \( \mathbf{P}(\mathbf{x}) \) & 0.2 & 0.5 & \( \boldsymbol{\alpha} \) & 0.1 \\
\hline
\end{tabular}
Compute each of the following quantities.
a. a
b. \( \mathrm{P}(0) \)
c. \( \mathrm{P}(\mathrm{X}>0) \)
d. \( P(X \geqslant 0) \)
e. \( P(X \leqslant-2) \)
f. The mean \( \mu \) of \( X \)
g. The variance \( \sigma^{2} \) of X
h. The standard deviation \( \sigma \) of X
