For the given probability density function, over the stated interval, find the requested value.
-$f ( x ) = \frac { 1 } { 2 } x$ over $[ 0,2 ] ;$ Find the median.
A) $\frac { 1 } { 2 }$
B) 2
C) $\sqrt { 2 }$
D) $\frac { 1 } { 4 }$

Question

Quizplus · Accepted Answer

The median of a probability density function is the value $m$ such that the integral of the function from the lower bound up to $m$ equals 0.5. For the given function $f(x) = \frac{1}{2}x$ over the interval $[0,2]$, we find the median by solving the equation $\int_{0}^{m} \frac{1}{2}x dx = 0.5$. Solving this equation gives $m = \sqrt{2}$.

For the Given Probability Density Function, Over the Stated Interval f(x)=12xf ( x ) = \frac { 1 } { 2 } xf(x)=21​x

For the Given Probability Density Function, Over the Stated Interval $f ( x ) = \frac { 1 } { 2 } x$