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Let X be a random variable that takes on values between 0 and c. That is...

Let X be a random variable that takes on values between 0 and c. That is P{0 ≤ X ≤ c} = 1. Show that V ar(X) ≤ c2

4
Hint: One approach is to first argue that E[X2] < cE[X] and then use this fact to show that

V ar(X) ≤ c2[α(1 − α)] where α = E[X]/c.

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