Prometheus Posted May 10, 2015 Share Posted May 10, 2015 So I want to find the Laplace transform of: [latex] f(t)=\alpha e^{-\alpha t} + \beta e^{-\beta t}[/latex] I make it: [latex]f^*(s)=\frac{\alpha}{\alpha+s}+\frac{\beta}{\beta+s}[/latex] Which I thought simply follows from the linearity of the integral operator. But according to my lecture notes it is: [latex] f^*(s)=(\frac{\alpha}{\alpha+s})(\frac{\beta}{\beta+s}) [/latex] I'm hoping there is a mistake in the lecture notes, otherwise I've totally misunderstood things. I would appreciate it if anyone could comment on which answer is correct. Link to comment Share on other sites More sharing options...
imatfaal Posted May 10, 2015 Share Posted May 10, 2015 http://www.wolframalpha.com/input/?i=laplace+transform+f%28t%29%3Dxe^{-yt}+%2B+ye^{-yt} 1 Link to comment Share on other sites More sharing options...
Prometheus Posted May 10, 2015 Author Share Posted May 10, 2015 Cheers. Good old wolfram alpha, didn't even occur to me to check there. Link to comment Share on other sites More sharing options...
Prometheus Posted May 19, 2015 Author Share Posted May 19, 2015 Turns out it was the product, not the sum. What I neglected to add was that I was dealing with random variables. I knew this was true for Gaussian random variables, but didn't know it extends to all random variables (which what it seems to be true, i'll have to find out exactly why, but I know it's related to convolution theorem). Link to comment Share on other sites More sharing options...
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