distribution is a discrete distribution closely related to the binomial distribution and so will be considered later. 1. orF example, the amount of time (beginning now) until an earthquake occurs has an exponential distribution. /Length 1863 7�Bv���t��)�o���m���ʮk�l��u�ofJ7������P�����-�͢����]E)��K�ͪ8g�͡�ڡ�=�M�έ�Z�G�Z���h�]���ե�0�����h�W%2�+��V�ޭ&P��U�+�8��ƺI�"HMё{2�8���A�#��j�'��U���eǷ��V0Z[�8�:t�y��~�$X*bR�s����V`� >5P�}�F3%�ۑi2�\{�!dG-޼�s�a�����R�}_���}�,1e��s���t�P��9]�� Hݏ��:����L�ctRBU�3x�T��@*(�:��%�W�� �D �Ӡt�F�:�>�ߏQi��D���"�òX�)�� ?�&&�ʰ��8y���g: lG Recall that Gaussian distribution is a member of the The exponential distribution is a probability distribution which represents the time between events in a Poisson process. ƥ�dq�$� =x��抇%��bGeM�]Qoa���ԥ��� Note: One should not be surprised that the joint pdf belongs to the exponen-tial family of distribution. >> +Xn (t) = λe −λt (λt) n−1 (n−1)!, gamma distribution with parameters n and λ. It can be shown for the exponential distribution that the mean is equal to the standard deviation; i.e., μ = σ = 1/λ Moreover, the exponential distribution is the only continuous distribution that is Example 18.3. 2. Suppose that this distribution is governed by the exponential distribution with mean 100,000. Example 1 Suppose X follows the exponential distribution with λ-1 If Y-yx find the pdf of Y. Consequently, the family of distributions ff(xjp);0 0 0 for x≤ 0, where λ>0 is called the rate of the distribution.

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