Conditional expectation of exponential random variable

  • #1
For an exponential random variable X with rate u What is E{X|X>a} where a is a scale value
from searching in internet I found that
E{X|X>a}=a+E{x}​
but I can not prove it
Help please
 

Answers and Replies

  • #2
mathman
Science Advisor
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It can be done by a straightforward integration.
∫xe-uxdx/∫e-uxdx with limits a,∞ for both the numerator and the denominator.
 
  • #3
Thanks for reply, it is correct but why??
 
  • #4
mathman
Science Advisor
7,891
460
The integral in the numerator (properly normalized) from 0 to ∞ is the definition of E(X) for an exponentially distributed random variable. Changing the limits to (a,∞) means assuming X>a. The denominator supplies the normalization.
 

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