| \[t^{n}f(t)\] |
\[{( - 1)}^{n}\frac{d^{n}F(r)}{dr^{n}}\] |
Used to find moments |
| \[e^{at}f(t)\] |
\[F(r - a)\] |
Discounting produces a shift in the transform distribution |
| \[f'(t)\] |
\[rF(r) - f(0)\] |
Derivative: Used to solve differential equations |
| \[f*g = \int_{0}^{t}{f(x)g(t - x)}\] |
\[F(r)G(r)\] |
Convolution: Sum of independent random variables |
| \[f*\delta(t - t_{0})\] |
\[e^{- rt_{0}}F(r)\] |
Shifted output, or delay |
| \[f*1\] |
\[\frac{F(r)}{r}\] |
Integral Operator |