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Let $Y$ be a random variable of density g. How could I compute the expectation

$E[Y|Y<a]$ ? Thank you in advance!

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If $P(Y<a)>0$ and $EY$ exists. $$E[Y|Y<a] = \frac{E[Y\cdot1_{\{Y<a\}}]}{P(Y<a)} = \frac{\int\limits_{-\infty}^a xg(x)dx}{\int\limits_{-\infty}^a g(x)dx}$$

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  • $\begingroup$ Didn't quite understand what $E[Y\cdot1_{Y<a}]$ means $\endgroup$ – Vizag Apr 19 at 22:22
  • $\begingroup$ @Vizag is it better now? $\endgroup$ – Jakobian Apr 19 at 23:48

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