Exercise 2: A Revised Rollback-Cost Budget — Possible Solution
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GIVEN (REVISED DISTRIBUTION)
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P(no rollback) = 0.85, cost $0
P(partial rollback) = 0.10, cost $3,000
P(full rollback) = 0.05, cost $40,000

STEP 1: CONFIRMING A VALID DISTRIBUTION
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0.85 + 0.10 + 0.05 = 1.0

STEP 2: RECOMPUTING E[X]
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E[X] = (0)(0.85) + (3000)(0.10) + (40000)(0.05)
     = 0 + 300 + 2000
     = $2,300

STEP 3: COMPARING TO STEP 4's ORIGINAL FIGURE
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Original E[X] (Step 4): $1,560
Revised E[X]: $2,300

The budget should INCREASE, from $1,560 to $2,300 - an increase of
$740. Even though the full-rollback probability only rose from 3% to
5% (a 2-percentage-point change), that shift was entirely funded by
reducing the much cheaper partial-rollback probability, and because
the full-rollback cost ($40,000) so dramatically outweighs the partial
-rollback cost ($3,000), even a small probability shift toward the
expensive outcome moves the expected cost substantially.

WHY THIS WORKS AS AN ANSWER
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The distribution is validated first, E[X] is recomputed using this
chapter's own Step 4 formula, and the comparison against the original
figure is made explicit with the exact dollar difference, explaining
why a small probability shift produced a disproportionately large
change in expected cost.