Question

Three discrete distribution were discussed in your textbook. Each was defined by a random variable that measured the number of successes. In order to apply these distributions, you must know which one to use. Describe the distinguishing characteristics for each distribution.

Answer 1

The distinguishing characteristics for three discrete distributions:

(1)

Binomial Distribution:

(i) The number of trial = n is finite and fixed

(ii) In every trial, there are only 2 possible outcomes, called success and failure

(iii) The trials are independent of each other.

(iv) The probability of success = p from trial to trial is constant and the probability of failure = q = 1 - p so that p + q = 1

(2)
Poisson Distribution:

Poisson Distribution is a limiting case of the Binomial Distribution under the conditions:
(i) The number of trials = n = is indefinitely large, n .

(ii) The constant probability of success = p for each trial ia indefinitely small. i.e., p

(iii) Mean = np = is finite, which is a parameter of the Poisson Distribution.

(3)

Geometric Distribution:

(i) The phenomenon being modeled is a sequence of independent trials.

(ii) In every trial, there are only 2 possible outcomes, called success and failure

(iii) The probability of success = p from trial to trial is constant and the probability of failure = q = 1 - p so that p + q = 1

The geometric random variable is the count of the number of failures before the first success.