Chapter 11 - Probability and Calculus - 11.2 Expected Value and Variance of Continuous Random Variables - 11.2 Exercises - Page 585: 15

a. m=5 b. 0

We are given $f(x)=\frac{1}{4}; [3;7]$ The expected value is $\mu=5$ a. The median is $\int^{m}_{3}f(x)dx = \frac{1}{2}$ $\int^{m}_{3}\frac{1}{4} dx= \frac{1}{2}$ $\frac{1}{4}m - \frac{3}{4}= \frac{1}{2}$ $m=5$ b. The probability between the mean and the median is: $P(5 \leq X \leq 5)=\int^{5}_{5}\frac{1}{4}dx =\frac{1}{4}x|^{5}_{5}=0$