# Question: Let X be a random variable that takes on values

Let X be a random variable that takes on values between 0 and c. That is, P{0 ≤ X ≤ c} = 1.

Show that

Var(X) ≤ c2/4

One approach is to first argue that

E[X2] ≤ cE[X]

and then use this inequality to show that

Var(X) ≤ c2[α(1 − α)] where α =E[X]/c

Show that

Var(X) ≤ c2/4

One approach is to first argue that

E[X2] ≤ cE[X]

and then use this inequality to show that

Var(X) ≤ c2[α(1 − α)] where α =E[X]/c

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