fixed characteristic function of uniform distribution
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$\frac{x-a}{b-a} \One_{[a,b]} + \One_{(b,\infty)}$ &
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$\frac{a+b}{2}$ &
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$\frac{(b-a)^2}{12}$ &
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$\frac{e^{\i t b} - e^{\i t a}}{t (b-a)}$\footnote{$\phi_X(0) = 1$ }&
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$\frac{e^{\i t b} - e^{\i t a}}{\i t (b-a)}$\footnote{$\phi_X(0) = 1$ }&
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$\frac{e^{t b} - e^{t a}}{t (b-a)}$\footnote{$M_X(0) = 1$}\\
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Exponential &
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$\Exp(\lambda)$ &
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