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anonymous
 4 years ago
Ok.\[f(x)=\left(\begin{matrix}ke ^{2x} \\ 0\end{matrix}\right)\] \[x \ge 0\]otherwise,
Find k
anonymous
 4 years ago
Ok.\[f(x)=\left(\begin{matrix}ke ^{2x} \\ 0\end{matrix}\right)\] \[x \ge 0\]otherwise, Find k

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ash2326
 4 years ago
Best ResponseYou've already chosen the best response.2Is this a probability density function?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Is it piece wise functions?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Just probability density.

ash2326
 4 years ago
Best ResponseYou've already chosen the best response.2integrate it between 0 to infinity, it's value is 1, you'll be able to find k

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I'm not sure how to integrate it from infinity... that's the problem I'm having.

ash2326
 4 years ago
Best ResponseYou've already chosen the best response.2we know for a probability density function \[\int_{\infty}^{\infty} f(x)=1\] now f(x)=ke^2x for x\(\ge\)0 \[\int_{0}^{\infty} f(x)=1\] so our integral becomes now f(x)=ke^2x now \[\int_{0}^{\infty} ke^{2x}=1\] integral of e^x=e^x so \[(\frac{1}{2}*k*e^{2x})=1\] now insert the limits e^(2x) as x>\(\infty\) is 0 so we get \[(0(1/2*k*e^0)=1\] or \[k/2=1\] or \[\large{k=2}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Yes... Just one question, How did (0(1/2*k*e^0)=1 become 2?

ash2326
 4 years ago
Best ResponseYou've already chosen the best response.2see we have, (0(1/2*k*e^0)=1 this is an equation now e^0=1 so (0+1/2k*1)=1 so k/2=1 or k=2

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Ah OK. I just figured that out :) Thanks!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0A computer ink cartridge has a life of X hours. The variable X is modelled by the probability density function \[f(x)=\left(\begin{matrix}kx^{2} \\ 0\end{matrix}\right) \]\[x \ge 0 otherwise \] (a) Find K
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