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

A continuous random variable is given by the following probability density function Let be the cumulative distribution function for the random variable Find for 
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Hint 

Recall that if is the probability density function of a random variable , its cumulative distribution function is defined as . 
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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 