17. A random variable ( X ) has a CDF such that [ F(x)=left{egin{array}{ll} x / 2 & 0<x leqslant 1 \ x-1 / 2 & 1<x leqslant 3 / 2 end{array} ight. ] (a) Graph ( F(x) ). (b) Graph the pdf ( f(x) ). (c) Find ( P[X leqslant 1 / 2] ). (d) Find ( P[X geqslant 1 / 2] ). (e) Find ( P[X leqslant 1.25] ). (f) What is ( P[X=1.25] ) ?
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- For \( 0 < x \leq 1 \), \( F(x) = \frac{x}{2} \). This is a straight line from (0,0) to (1,0.5). - For \( 1 < x \leq \frac{3}{2} \), \( F(x) = x - \frac{1}{2} \). This is a straight line from (1,0.5) to \((\frac{3}{2},1)\). Show more…
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