The answer is:
a) Gives you the expected value when you have different probabilities for different outcomes outcomes. Like if you were given a probablty table and had to compute the expected value.
b) E(X) = ∑{X * P(X)}
c) You are adding the sum of all the outcomes multiplied by each their individual probabilities for each outcome instead of just one probability.
d) Answer is -$2.50. That is if you spend the $10 for a chance to win $15,000 on average or more than likely you should expect to lose $2.50.
The expected value, also known as expectation, expectancy, mathematical expectation, mean, average, or first moment, is a generalization of the weighted average in the field of probability theory. Informally, the anticipated value is the arithmetic mean of a significant number of outcomes of a random variable that were independently chosen.
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