Question

In comparing probability distributions, which of the following statements is TRUE?

Select one:

1. The geometric and Poisson distributions have the lack of memory property.

2. The exponential and Poisson distributions are interchangeable because they have the exact same
random variable.

3. The geometric and negative binomial distributions both have a random number of trials.

4. The uniform and normal distributions have the same distribution shapes.

5. The Poisson distribution is the limiting form of the negative binomial distribution.

Answer 1

1. False, Among all the continuous distributions only the exponential distributions have the lack.of memory property.

2. True, Poisson distribution deals with the number of occurrences in a fixed period of time, while the exponential distribution deals with the time between occurrences of successive events as time flows by continuously. So, there's a relationship here. And also the random variable used is same.

3. True, the geometric distribution is a special case of negative binomial distribution both have random number of trails. In negative binomial we have a count of successes from repeated counts in a experiment while geometric we repeat number of trails for a single success.

4. False, Normal distribution have the bell shape curve and the uniform distribution have the rectangular distribution

5. True, Poisson distribution can be expressed as a limiting case of negative binomial distribution. In a series of trails for success or failure then a parameter is introduced to indicate the number of failures that stops the count.