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E[X | X > 0] for a standard normal

MediumStatisticsCalculus~6m

For X∼N(0,1)X\sim N(0,1), compute E[X∣X>0]E[X \mid X>0]. (to 3 decimals)

Show hints (2)+
  1. Substitute u=x2/2u=x^2/2 in the numerator integral.
  2. Divide by P(X>0)=12P(X>0)=\tfrac12.

Answer

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0.798 (± 0.01)

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