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Q14Section A (Section A)14 of 35

Interval probability from a mixed distribution function

The distribution function of a random variable XX is given by

F(x)={0,x<0, 14,0≤x<14, 12,14≤x<12, 34,12≤x<34, x+35,34≤x<2, 1,x≥2.F(x)=\begin{cases}0, & x<0,\ \frac14, & 0\le x<\frac14,\ \frac12, & \frac14\le x<\frac12,\ \frac34, & \frac12\le x<\frac34,\ \frac{x+3}5, & \frac34\le x<2,\ 1, & x\ge2.\end{cases}

Then P(14≤X≤1)P\left(\frac14\le X\le1\right) is

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