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Competitive Stats
Q33Section I (Objective (Q1–Q80))33 of 80

Probability — parameter range for a valid piecewise c.d.f.

The function

F(x)={0,x<0 x2,0≤x<1 (1−α)x+2α−1,1≤x<2 1,x≥2F(x) = \begin{cases} 0, & x<0 \ \dfrac{x}{2}, & 0 \le x < 1 \ (1-\alpha)x + 2\alpha - 1, & 1 \le x < 2 \ 1, & x \ge 2 \end{cases}

is a distribution function if and only if

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