MATH105 April 2015
• 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 (a) • Q2 (b) • Q3 (a) • Q3 (b) • Q4 (a) • Q4 (b) • Q5 (a) • Q5 (b) • Q5 (c) • Q5 (d) • Q6 (a) • Q6 (b) •
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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Recall that if is the probability density function of a random variable , its cumulative distribution function is defined as .
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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,
Putting all these results together means that the cumulative distribution function for the random variable in the range is