All my work is wrong, except for what's in red. can you please work it out step by step
Homework Answers
a) f(x)=cx^2+x, We know Integrate(f(x)dx)=1, thus (cx^2+x)dx=1 [You pulled the constant c out but it is attached only with x^2] or cx^3/x+x^2/2|(0,1)=1, which gives
c/3+1/2=1 or c/3=1/2 and c=3/2.
b)E(x)=x*f(x)dx from (0,1) or (3/2*x^3+x^2)dx=3/8*x^4+x^3/3|(0,1)=3/8+1/3=17/24=0.708
c) Var(x)=E(x^2)-(E(x))^2. E(x^2)=x^2f(x)dx=(3/2*x^4+x^3)dx=3/10*x^5+x^4/4|(0,1)=3/10+1/4=11/20
Thus Var(x)=11/20-(17/24)^2=0.048
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All my work is wrong, except for what's in red. can
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explanation?
Thanks!
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