Preliminary Course
Applied Mathematics
Probabilities. Geometrical Law
Geometric Distribution
Consider again a sequence of Bernoulli trials X = (X1, X2, ... ) with success parameter p ∈ [0,1].
We are interested in the random variable N that gives the trial number of the first success:
N = min { n ∈ N+, Xn = 1 }
P (N = n ) = p (1-p) n-1
This probability rule, applied to n=1,... max defines a geometric distribution.
The sequence of probabilities builds a geometric sequence.
Properties:
E[N] = 1 / p
VAR[N] = (1-p) / p2