Question

Discuss the difference between the Poisson and Hyper-geometric probability distribution. When would each of these be used? Describe a scenario for each.

Answer 1

POISSON DISTRIBUTION:

Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate and independently of the time since the last event. The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume.

Applications of Poisson distribution:

1. The distribution of the number of road accidents on a busy road per minute
2. The distribution of the number of radioactive elements per minute in a fusion process

Example problem: On a certain road in a 15 day period, on average there are 12 crashes. What is the probability that on a given week there are 3 crashes?

HYPER GEOMETRIC DISTRIBUTION:

Hypergeometric distribution is a discrete probability distribution that describes the probability of ‘k’ successes in ‘n’ draws, without replacement, from a finite population of size N that contains exactly ‘m’ objects with that feature, wherein each draw is either a success or a failure.

Applications of Hypergeometric distribution:

1. Estimation of number of fishes in a lake

Example problem: On a certain road crashes occurred on 12 out of 15 days. We pick one week out of this 15 days period, what is the probability that there are 2 days with crashes?