Answers
1)for this to be valid: f(x)dx =
c*(1-x6) dx =c*(x-x7/7) |1-1 =c*12/7=1
c=7/12
2)
E(X)= xf(x)dx =
(7/12)*(x-x7) dx =c*(x2/2-x8/8) |1-1 =0
E(X2) = x2f(x)dx =
(7/12)*(x2-x8) dx =c*(x3/3-x9/9) |1-1=7/27
therefore Var(X)=E(X2)-(E(X))2 =7/27-02=7/27
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