Question 349491
a) Integrate to find the CDF.
PDF={{{(1/3)}}} {{{0<=x<1}}}
PDF={{{(2/3)}}} {{{1<=x<=2}}}
Integrating,
CDF={{{(1/3)x+C[1]}}} {{{0<=x<1}}}
CDF={{{(2/3)x+C[2]}}} {{{1<=x<=2}}}
Solve for the constants using conditions,
{{{CDF(0)=0}}}
{{{(1/3)(0)+C[1]=0}}}
{{{C[1]=0}}}
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{{{CDF(2)=1}}}
{{{(2/3)(2)+C[2]=1}}}
{{{C[2]=-1/3}}}
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CDF={{{(1/3)x}}} {{{0<=x<1}}}
CDF={{{(2/3)x-1/3}}} {{{1<=x<=2}}}
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b) Median=1