Find the median (another measure of average) for a random variable with pdf on The median is the 50% mark on probability, that is, the value such that

Question

Find the median (another measure of average) for a random variable with pdf  on  The median is the 50% mark on probability, that is, the value  such that

Quizplus · Accepted Answer

To find the median, we need to solve the equation:
$$\int_{-\infty}^{m} 11e^{-ax^2} dx = \frac{1}{2}$$
We know that $\int_{-\infty}^{m}11e^{-ax^2} dx $  is the cumulative distribution function evaluated at $m$ , hence we can write the equation above as 
$$\Phi(m) = \int_{-\infty}^{m} 11e^{-ax^2} dx = \frac{1}{2}$$
Using a table of normal distribution, we can find that the closest value of $\Phi(m)$  to  $\frac{1}{2}$ is $\Phi(m)\approx 0.477$, which corresponds to $m\approx 0.08 = \boxed{	extbf{(B) }11eaa88b	ext{_}9152	ext{_}9436	ext{_}a696	ext{_}5d6ae721ecd3	ext{_}TB5869	ext{_}11}}$.

Find the Median (Another Measure of Average) for a Random