Question 349782
a){{{int(f(x),dx,0,1)=1}}}
{{{int(kx^2,dx,0,1)=1}}}
{{{(kx^3)/3=1}}} from {{{x=0}}} to {{{x=1}}}
{{{k/3=1}}}
{{{k=3}}}
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b) {{{E(x)=int(x*f(x),dx,0,1)}}}
{{{E(x)=int(3x^3,dx,0,1)}}}
{{{E(x)=(3/4)x^4}}} from {{{x=0}}} to {{{x=1}}}
{{{E(x)=mu=3/4}}}
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c) {{{V(x)=int((x-mu)^2*f(x),dx,0,1)}}}
{{{V(x)=int((x-3/4)^2*3x^2,dx,0,1)}}}
{{{V(x)=int((3x^4-(9/2)x^3+(27/4)x^2),dx,0,1)}}}
{{{V(x)=(3/5)x^5-(9/4)x^4+(27/8)x^3)}}} from {{{x=0}}} to {{{x=1}}}
{{{V(x)=3/5-9/4+27/8}}}
{{{V(x)=3/80}}}