MATH101 April 2007
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Question 01 (g)
An exponentially distributed continuous random variable X has probability density function for , where k is a positive constant. The median value of X equals 10. Find k.
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!
The definition of the median is the number m such that
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As in the hint, we have that the median m is the number such that
We are told that m=10. Hence, evaluating this integral gives
Solving for k yields
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MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Probability density function, Pages using DynamicPageList parser function, Pages using DynamicPageList parser tag