Discrete Distributions

Posted: August 27th, 2021

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Discrete Distributions

Poisson Distribution

1. Example

The example case is the use of Poisson distribution in maternity hospitals to help calculate the number of births expected in a given night. The number of deliveries in a hospital is estimated to be 3,000 per year. If the case happened randomly throughout the period, about 1,000 deliveries are expected between midnight hours and at around 9.00 am. However, during this time, many staffs are off-duty. Hence, the hospital must ensure that there are enough staffs to attend to the situation at any given time. From the case, the average deliveries per particular night are;

, in this case, the probability of having a delivery activity is 0, 1, 2… babies per night which can be estimated through Poisson distribution. The probabilities are as follows;

According to the equation, five (5) or more deliveries in a year would be expected fifty-two (52) times in a year. The greatest number of deliveries in any night per year is eight (8). However, this pattern will only follow Poisson distribution if deliveries were random throughout 24 hours (Robert et al.). The discrete variable is the number of deliveries, taking values 0, 1, 2, 3… with a mean of 2.74 with 52 trials. Thus, the probability of success is having a delivery incident while failure is reporting no delivery incident.

1. This Satisfies the Requirements of Poisson Distribution Because:
2. The occurrence of one delivery does not affect the occurrence of any other event (Robert et al.).
3. The occurrence of any delivery activity can take a value of 0, 1, 2, …
4. Probabilities

EXACT 1

ATLEAST 1

P (1) + p (2) + p (3) —

= 0.177+0.242 + 0.221 = 0.64

ATMOST 1

P (1) – P (0) = 0.177 – 0.065 = 0.112

1. Expected Value

E(X) =n∑i=1xip(xi)

Where n = 4, i=0,1,2,3,

• Standard Deviation

Std. dev =

Works Cited

Robert, Kissell, et al. “Poisson Distribution.” ScienceDirect.com | Science, Health and Medical Journals, Full-Text Articles and Books, Elsevier B.V., 2017, www.sciencedirect.com/topics/mathematics/poisson-distribution. Accessed 16 Feb. 2021.