Science:Math Exam Resources/Courses/MATH105/April 2012/Question 04 (a)
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Question 04 (a) 

Consider the function (a) Find the values of a, k and b for which F is a valid cummulative distribution function of a continuous random variable. Then sketch the graph of F. 
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 

A cumulative distribution function F of a continuous random variable must satisfy the following:

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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Following the definition of a cdf (see the hint), we compute
and
Therefore k = 1/(arctan 1), or simply .
Hence our final answer is
As a remark, it is important to know the exact trig values for special angles. Here: so . 