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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.

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

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  • 4
    $\begingroup$ 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 $m$ $\endgroup$ – lulu Nov 21 '16 at 22:10
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    $\begingroup$ You may want to have a look a exponential distributions. $\endgroup$ – A.G. Nov 21 '16 at 22:13
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    $\begingroup$ You can also search this site with keywords "median distribution random variable"... $\endgroup$ – A.G. Nov 21 '16 at 22:15
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The median is located where the $\text{cdf}$ reaches $1/2$.

Integrating,

$$\text{cdf}(x)=\int_0^x\text{pdf}(x) dx=\int_0^x0.06e^{-0.06x}dx=-\left.e^{-0.06x}\right|_0^x=\frac12.$$

I let you the conclude.

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  • $\begingroup$ Is the answer then .5309? $\endgroup$ – user344249 Nov 21 '16 at 22:19
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    $\begingroup$ Probably not. How do you get this value ? $\endgroup$ – Yves Daoust Nov 21 '16 at 22:20
  • $\begingroup$ Wait I did it wrong, I should have actually done ln(.5)/(-.06) and that would then give me the answer of 11.5525 which is correct $\endgroup$ – user344249 Nov 21 '16 at 22:23
  • $\begingroup$ Thank you so much for your help $\endgroup$ – user344249 Nov 21 '16 at 22:23

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