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I don't really understand the difference between exponential and geometric distribution.

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Did you try looking at Wikipedia?

The exponential distribution may be viewed as a continuous counterpart of the geometric distribution, which describes the number of Bernoulli trials necessary for a discrete process to change state. In contrast, the exponential distribution describes the time for a continuous process to change state.

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The geometric distribution belongs to the exponential family and so does "the exponential distribution". They only differ in the parameters and sufficient statistics used in factored expression for conditional distributions from the exponential family.

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    $\begingroup$ Welcome to the site! Saying they "only differ" sounds a little strong, particularly since the sets of values they can take on are quite different. :) $\endgroup$ – cardinal Oct 21 '11 at 9:53
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Exponential distributions involve raising numbers to a certain power whereas geometric distributions are more general in nature and involve performing various operations on numbers such as multiplying a certain number by two continuously. Exponential distributions are more specific types of geometric distributions.

Exponential distributions: 2, 4, 16, 256 or 3, 9, 81, 6561.

Geometric distribution: 2, 4, 8, 16, 32, 64.

Just my two cents anyway.

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    $\begingroup$ Because you use "exponential distribution" in a non-standard way here, your answer is likely to be misunderstood until you edit it to explain what you mean by exponential distribution. $\endgroup$ – whuber Oct 6 '14 at 17:53
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    $\begingroup$ +1 to whuber's comment above. For what it's worth, people typically call the geometric distribution a special case of the exponential because the latter is defined only on integers. For example, if $X$ is an exponentially distributed r.v., with parameter $\lambda$ then $\lfloor X\rfloor$ is a geometrically distributed r.v. with parameter $p=1-e^{-\lambda}$ $\endgroup$ – Matt Krause Sep 30 '15 at 0:24
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    $\begingroup$ I think this post is very misleading, the given examples appear to make no sense. (-1) $\endgroup$ – Silverfish Sep 30 '15 at 0:43

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