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!set gl_author=Sophie, Lemaire
!set gl_keywords=continuous_probability_distribution
!set gl_title=
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<div class="wims_defn"><h4>Definition</h4>
Let \(a) be a positive real. The <span class="wims_emph">exponential
distribution</span> with parameter \(a)</span> (denoted by
\(\mathcal{E}(a))) is a continuous distribution over \(\RR_+) with
density function

<div class="wimscenter">
\(x\mapsto a e^{-a x}1_{x>0} )
</div>
</div>
<table class="wimsborder wimscenter">
<tr><th>Expectation</th><th>Variance</th><th>Characteristic function</th></tr>
<td>\(\frac{1}{a})</td><td>\(\frac{1}{a^2})</td><td>\(\frac{1}{1-i\frac{t}{a}})</td></tr></table>
