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 (a)
A continuous random variable is given by the following probability density function
Find the expected value of the random variable .
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Recall the definition of expected value: if is the probability density function of a random variable , its expected value is defined as the integral .
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To compute , we will compute the integral , where is the probability density function of .
Since for all and .
Since for and for ,
Note that we could have also obtained this result by simply noting that the integrand is an odd function, and if is an odd function, for any .