PMF of Bernoulli trials needed to produce at least one success and at least one failure

Asked Apr 26 '16 at 01:10

Active Apr 26 '16 at 01:10

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Let X be the number of Bernoulli(p) trials until we get at least one success and at least one failure.

This means we need a string of successes followed by a failure or a string of failures followed by a success.

$P(X = k) = p^{k-1}(1-p) + (1-p)^{k-1}p\quad\quad$ with support $k \geq 2$

Is this correct?
This is similar to but is not the Geometric distribution.
Is there a name for this distribution?

asked Apr 26 '16 at 01:10

user137481

Yes, it is correct, for $0\lt p\lt 1$. – André Nicolas Apr 26 '16 at 01:14
@AndréNicolas Is there a name for this distribution? – user137481 Apr 26 '16 at 01:15
I do not know of a name. – André Nicolas Apr 26 '16 at 01:18
@AndréNicolas Thanks anyway. – user137481 Apr 26 '16 at 01:19

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