To find the expected value \( E(X) \) of a random variable \( X \) given its probability distribution, we use the formula:
\[ E(X) = \sum (x \cdot P(X = x)) \]
Where \( x \) represents the possible values of the random variable \( X \), and \( P(X = x) \) is the probability of each value.
Given the table you provided:
\[ \begin{array}{|c|c|} \hline X & P(X) \ \hline 0 & 0.4 \ 1 & 0.3 \ -1 & 0.3 \ \hline \end{array} \]
We calculate the expected value as follows:
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For \( x = 0 \): \[ 0 \cdot P(X=0) = 0 \cdot 0.4 = 0 \]
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For \( x = 1 \): \[ 1 \cdot P(X=1) = 1 \cdot 0.3 = 0.3 \]
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For \( x = -1 \): \[ -1 \cdot P(X=-1) = -1 \cdot 0.3 = -0.3 \]
Now, we sum these results: \[ E(X) = 0 + 0.3 - 0.3 = 0 \]
Therefore, the expected value of \( X \) is
\[ \boxed{0} \]