Science:Math Exam Resources/Courses/MATH105/April 2010/Question 01 (m)
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q1 (g) • Q1 (h) • Q1 (i) • Q1 (j) • Q1 (k) • Q1 (l) • Q1 (m) • Q1 (n) • Q2 • Q3 • Q4 • Q5 (a) • Q5 (b) • Q5 (c) • Q6 •
Question 01 (m) 

Compute the cumulative distribution function corresponding to the density function 
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 cumulative distribution function, , can be obtained by integrating the probability density function from negative infinity to . i.e: 
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 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. The cumulative distribution function, , can be obtained by integrating the probability density function from negative infinity to . i.e: (Note that we can assume that if or ). Applying the defintion of the cumulative distribution to this problem gives: Simplifying gives: 