For the given probability density function, over the stated interval, find the requested value.
-$f ( x ) = \left\{ \begin{array} { l l } \frac { 7 } { x ^ { 2 } } & 1 \leq x \leq \frac { 7 } { 6 } \ 0 \quad & \text { Otherwise } \end{array} ; \right.$ Find the median.
A) $7 \ln \left( \frac { 7 } { 6 } \right)$
B) $\frac { 1 } { 2 }$
C) $\frac { 7 } { 12 }$
D) $\frac { 14 } { 13 }$

Question

Quizplus · Accepted Answer

The median $m$ of a probability density function is found by solving the equation $\int_{a}^{m} f(x) dx = 0.5$, where $a$ is the lower limit of the interval. For the given function, this translates to solving $\int_{1}^{m} \frac{7}{x^2} dx = 0.5$. Solving this integral and equation leads to $m = \frac{14}{13}$.

For the Given Probability Density Function, Over the Stated Interval