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I need to solve for general and cont. diff. pdf $g(x)$

$$\frac{d}{db} \int_0^b xg(x)dx$$

Standard Leibnitz rule would give me

$$b g(b) + \int_0^b 0 dx$$

the result makes sense - but I'm not sure whether Leibnitz is applicable here.

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  • $\begingroup$ I think your interpretation of the formula is wrong! (it lakcs a division by $P(X \le b)= \int_0^b g(x) \; dx$. Can you correct? $\endgroup$ Feb 20, 2015 at 15:52
  • $\begingroup$ hint: $bg(b)$ (as the formula stands uncorrected) $\endgroup$ Feb 20, 2015 at 15:54
  • $\begingroup$ Alright, thank you. I guess given your hint that Leibnitz is indeed applicable. $\endgroup$
    – FooBar
    Feb 20, 2015 at 15:56
  • $\begingroup$ ¨Just write out the definition of the derivative as a limit ... $\endgroup$ Feb 20, 2015 at 15:57

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