Science:Math Exam Resources/Courses/MATH101/April 2007/Question 01 (g)
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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! 
Hint 

The definition of the median is the number m such that 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. 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 and thus 