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Answer :
The expected value (or mean) of X is -2.5.
Expected value or the mean is a statistical measure of central tendency that takes into account the probabilities of each possible outcome. It is the sum of each possible outcome multiplied by its probability. The formula for expected value is:
Expected Value (E) = ∑ [Xi * P(Xi)]
Here, the probability distribution table for the random variable X is given:
x P(x)
100 0.2
25 0.2
25 0.5
100 0.1
Thus,
Expected value (E) of X = (-100 * 0.2) + (-25 * 0.2) + (25 * 0.5) + (100 * 0.1)= -20 - 5 + 12.5 + 10
= -2.5
Therefore, the expected value or the mean of X is -2.5.
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