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Q106Section III (Statistics)106 of 180

Reading probability off a piecewise CDF, including a jump

The distribution of a random variable X is given by the piecewise CDF F(x)=0,14,12,34,x+35,1F(x)=0,\tfrac14,\tfrac12,\tfrac34,\tfrac{x+3}5,1 on the successive intervals (−∞,0),[0,14),[14,12),[12,34),[34,2),[2,∞)(-\infty,0),[0,\tfrac14),[\tfrac14,\tfrac12), [\tfrac12,\tfrac34),[\tfrac34,2),[2,\infty). Then P[12≤X≤34]P\left[\tfrac12\le X\le\tfrac34\right] is:

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