Mathematics, 14.06.2021 19:40 aapowell1
Let x be a continuous random variable over [a, b] with probability density function f. Then the median of the x-values is that number m for which ModifyingBelow Integral from a to m f (x )font size decreased by 6 dx With font size decreased by 4equalsone half . Find the median. f(x)equalsk e Superscript negative kx, [0,infinity)
Answers: 3
".![\int^{m}_{a}\ f(x)\ dx=\frac{1}{2}\\\\f(x)=ke^{-kx}, \ [0, \infty]\\\\](/tpl/images/1374/1671/cea15.png)
![so,\\\\ \int^{m}_{a}\ f(x)\ dx=\frac{1}{2}\\\\\to \int^m_0 k\cdot e^{-kx}=\frac{1}{2}\\\\\to [\frac{k\cdot e^{-kx}}{-k}]^m_0=\frac{1}{2}\\\\\to [- e^{-kx}]^m_0=\frac{1}{2}\\\\\to - e^{-km} +1=\frac{1}{2}\\\\\to e^{-km} =\frac{1}{2}\\\\\to e^{km} =2\\\\\to \ln(e^{km}) =\ln 2\\\\\to km= \ln \ 2\\\\\to m=\frac{\ln \ 2}{k}\\\\ \text{the answer is: } \\\\ \to \int e^{ax}\ dx=\frac{e^{ax}}{a}+c](/tpl/images/1374/1671/624fe.png)
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Let x be a continuous random variable over [a, b] with probability density function f. Then the med...
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