Exercise 1: Expected Monthly Signups — Possible Solution
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GIVEN
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P(X=100) = 0.5
P(X=200) = 0.3
P(X=500) = 0.2

STEP 1: CONFIRMING A VALID DISTRIBUTION
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0.5 + 0.3 + 0.2 = 1.0

The probabilities sum to exactly 1, confirming this is a valid
distribution per this chapter's own requirement (and Chapter 2's own
certainty axiom).

STEP 2: COMPUTING E[X]
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E[X] = (100)(0.5) + (200)(0.3) + (500)(0.2)
     = 50 + 60 + 100
     = 210

The expected number of monthly signups is 210.

WHY THIS WORKS AS AN ANSWER
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The distribution is validated first per this chapter's own
requirement that the probabilities sum to 1, and the expected value
is computed by directly applying this chapter's own formula - summing
each outcome multiplied by its own probability - rather than simply
averaging the three raw values without weighting them by probability.