Question

In: Statistics and Probability

How can you write the geometric distribution into an exponential distribution? For the geometric distribution: P(y;...

How can you write the geometric distribution into an exponential distribution?

For the geometric distribution: P(y; p) = p(1 − p) ^ y−1

for y = 1,2, ⋯ and 0 < p < 1.

Expert Solution

The exponential distribution may be viewed as a continuous counterpart of the geometric distribution.

For the geometric distribution: for y = 1,2, ⋯ and 0 < p < 1.

The CDF of geometric distribution is,

for y = 1,2, ⋯ and 0 < p < 1.

Let the interval of y be divided into n equal intervals of length t. Then y = nt

Let the number of occurrence of event be in n time interval. Then p = /n

For continuous distribution,

which is the CDF of exponential distribution.

Using the below limit formula,

Thus, the continuous distribution of geometric distribution is exponential distribution

orchestra answered 2 years ago

how can I know if my problem is of the geometric distribution problem?

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