%���� +Xn (t) = λe −λt (λt) n−1 (n−1)!, gamma distribution with parameters n and λ. 2. The exponential distribution The exponential distribution is defined by f(t) = λe−λt t ≥ 0 λ a constant or sometimes (see the Section on Reliability in 46) by f(t) = 1 µ e−t/µ t ≥ 0 µ a constant The advantage of this latter representation is that it may be shown that the mean of the distribution is µ. Note: One should not be surprised that the joint pdf belongs to the exponen-tial family of distribution. Example 18.3. Moments of the exponential distribution. 1. 4. For example, we might measure the number of miles traveled by a given car before its transmission ceases to function. 5 0 obj << >> It is the constant counterpart of the geometric distribution, which is rather discrete. Consequently, the family of distributions ff(xjp);0 .

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