Science:Math Exam Resources/Courses/MATH105/April 2015/Question 04 (b)
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Question 04 (b) |
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A continuous random variable is given by the following probability density function Let be the cumulative distribution function for the random variable Find for |
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 |
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Recall that if is the probability density function of a random variable , its cumulative distribution function is defined as . |
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.
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Solution |
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Please rate my easiness! It's quick and helps everyone guide their studies. The cumulative distribution function of a random variable is defined as , where is the probability density function of . Suppose . Then Since for all , For Therefore, For , Therefore, Putting all these results together means that the cumulative distribution function for the random variable in the range is |