The cumulative distribution for a random variable x is
F(x) = 1/2 sqrt x-1; 1≤x≤5
Calculate the probabilities
Pr(1≤x≤4.1)
Given the cumulative distribution,
F(x)=1/2(x−1)F(x)=1/2(\sqrt{x-1})F(x)=1/2(x−1), we can determine the p(1⩽x⩽4.1)p(1\leqslant x\leqslant 4.1)p(1⩽x⩽4.1) as follows.
p(1⩽x⩽4.1)=F(4.1)−F(1)p(1\leqslant x\leqslant4.1)=F(4.1)-F(1)p(1⩽x⩽4.1)=F(4.1)−F(1)
Now,
F(4.1)=(4.1−1)/2=3.1/2=0.88034084F(4.1)=(\sqrt{4.1-1})/2=\sqrt{3.1}/2=0.88034084F(4.1)=(4.1−1)/2=3.1/2=0.88034084 and F(1)=(1−1)/2=0F(1)=(\sqrt{1-1})/2=0F(1)=(1−1)/2=0
Therefore,
p(1⩽x⩽4.1)=F(4.1)−F(1)=0.88034084−0=0.88034084p(1\leqslant x\leqslant4.1)=F(4.1)-F(1)=0.88034084-0=0.88034084p(1⩽x⩽4.1)=F(4.1)−F(1)=0.88034084−0=0.88034084
Thus, pr(1⩽x⩽4.1)=0.8803(4dp)pr(1\leqslant x\leqslant 4.1)=0.8803(4dp)pr(1⩽x⩽4.1)=0.8803(4dp)
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