Science:Math Exam Resources/Courses/MATH105/April 2018/Question 05 (c)
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Question 05 (c) 

According to sociologists, the net income of the people can be modelled with a continuous random variable , which has the following CDF:
where and are positive constants and ( is the minimum income and is the tail index).
(c) For which values of does the random variable has a finite expected value? 
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Hint 

Recall that the expected value of is , where is PDF. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. By the Hint, it is enough to find which make the integral converges. Recall the PDF found in part (a): Plugging this into the integral, we get
if . i.e., .
Therefore, the random variable has a finite expected value for . Answer: 