# How to find the median of a random variable given its probability density function? [closed]

Find the median of the random variable with the probability density function given below. (Round your answer to four decimal places.)

$$f(x) = 0.06\, e^{−0.06\,x}\text{ on }[0, +\infty)$$

Any help solving this problem would be greatly appreciated as I am extremely confused on where to even start.

## closed as off-topic by Did, user251257, Namaste, Shailesh, JonMark PerryNov 22 '16 at 5:21

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• Hint: the median is the value $m$ such that $P(x≤m)=\frac 12$ So, just compute $P(x≤m)$ for variable $m$ and solve for $m$ – lulu Nov 21 '16 at 22:10
• You may want to have a look a exponential distributions. – A.G. Nov 21 '16 at 22:13
• You can also search this site with keywords "median distribution random variable"... – A.G. Nov 21 '16 at 22:15

The median is located where the $\text{cdf}$ reaches $1/2$.
$$\text{cdf}(x)=\int_0^x\text{pdf}(x) dx=\int_0^x0.06e^{-0.06x}dx=-\left.e^{-0.06x}\right|_0^x=\frac12.$$