Question

The probability distribution of a random variable \( X \) is given by:

Then \( E(X) \) of distribution is:

• A. \( -1.8 \)
• B. \( -1 \)
• C. \( 1 \)
• D. \( 1.8 \)

Hint:

To find the expected value, multiply each possible value of \( X \) by its corresponding probability and sum the results.

Answer 1

The Correct Option is A

To solve the problem, we need to compute the expected value \( E(X) \) of the given discrete probability distribution.

1. Use the Formula for Expected Value:
The expected value \( E(X) \) is given by:
\( E(X) = \sum [x_i \cdot P(x_i)] \)

2. Substitute the Given Values:
\[ E(X) = (-4)(0.1) + (-3)(0.2) + (-2)(0.3) + (-1)(0.2) + (0)(0.2) \]
\[ = -0.4 + (-0.6) + (-0.6) + (-0.2) + 0 \]
\[ = -0.4 - 0.6 - 0.6 - 0.2 = -1.8 \]

3. Conclusion:
The expected value of the distribution is \( -1.8 \)

Final Answer:
The correct option is (A) -1.8.