Question:
The probability distribution of a random variable \( X \) is given by:
The probability distribution of a random variable \( X \) is given by:
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To find the expected value, multiply each possible value of \( X \) by its corresponding probability and sum the results.
Updated On: Mar 8, 2025
- \( -1.8 \)
- \( -1 \)
- \( 1 \)
- \( 1.8 \)
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The Correct Option is A
Solution and Explanation
The expected value \( E(X) \) of a random variable is given by:
\[
E(X) = \sum_{i} x_i \cdot P(x_i)
\]
Substituting the given values:
\[
E(X) = (-4 \cdot 0.1) + (-3 \cdot 0.2) + (-2 \cdot 0.3) + (-1 \cdot 0.2) + (0 \cdot 0.2)
\]
\[
E(X) = -0.4 - 0.6 - 0.6 - 0.2 + 0 = -1.8
\]
Thus, \( E(X) = -1.8 \).
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