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Random Variables and Distributions
Expectation and variance of a random variable
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Let \( X \) be a random variable with the following probability distribution.
\begin{tabular}{|c|c|}
\hline Value \( x \) of \( X \) & \( P(X=x) \) \\
\hline-30 & 0.10 \\
\hline-20 & 0.15 \\
\hline-10 & 0.20 \\
\hline 0 & 0.30 \\
\hline 10 & 0.25 \\
\hline
\end{tabular}
Complete the following. (If necessary, consult a list of formulas.)
(a) Find the expectation \( E(X) \) of \( X \).
\[
E(X)=\square
\]
(b) Find the variance \( \operatorname{Var}(X) \) of \( X \).
\[
\operatorname{Var}(X)=\square
\]
Explanation
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