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Mean of Random Variable or Expectation =  Σx.f(x)  

Now, sum of function from (0,1) can be interpreted as area under the curve so we can perform integration.

So Σx.f(x) = $\int_{0}^{1}x(6x(1+x))/5$ 
 

solving the integral for limits (simple calculation) we get Answer = 0.7

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