Science:Math Exam Resources/Courses/MATH105/April 2015/Question 04 (a)
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Question 04 (a) 

A continuous random variable is given by the following probability density function Find the expected value of the random variable . 
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 

Recall the definition of expected value: if is the probability density function of a random variable , its expected value is defined as the integral . 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. To compute , we will compute the integral , where is the probability density function of . Since for all and . Since for and for , Hence . Note that we could have also obtained this result by simply noting that the integrand is an odd function, and if is an odd function, for any . 