7. Suppose that Y1,...,Yn are i.i.d. with a uniform distribution on the interval (0,1), with density function

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7. Suppose that Y1,...,Yn are i.i.d. with a uniform distribution on the interval (0,1), with density function f and distribution function F defined as f(x) =  1 if x ∈ (0, 1), 0 otherwise, and F(x) =

0 if x ≤ 0, x if x ∈ (0, 1), 1 if x ≥ 1.

Use Result 4.1 to conclude which sample quantile q will have the smallest variance?

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