8. Let X be a random variable that takes on values between 0 and c. That is,
Question:
8. Let X be a random variable that takes on values between 0 and
c. That is, P[0≤ X ≤ c] = 1. Show that
$$Var(X) ≤ \frac{c^2}{4}$$
HINT: One approach is to first argue that
$$E[X^2] ≤ cE[X]$$
Then use this to show that
$$Var(X) = c^2[α(1-α)]$$ where α =
E[X]
/ c
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