Bahria University Lahore Campus
Course: Project Risk Management
(Spring 2020)
Instructor: Dr. Shahid Iqbal
Student: Muhammad Haseeb Khan
Enrollment# 085
Weekly Assignment # 07
What are “Discrete Probability Distributions” where do they come from and which is better
mentioned with examples?
Discrete Probability Distributions
Discrete Probability Distributions vs Continuous Probability distribution
Discrete probability distribution constitutes random variables whereas continuous probability
distribution comes from random continuous variables. Variables in discrete probability
distribution are countable whereas variables in continuous probability distribution are
measurable. Variables here refer to letter ‘x’ which represents quantitative (numerical variable)
and is usually observed in probability distribution experiment.
In other words, discrete probability distribution contains discrete data which only takes values
in in range whereas continuous probability distribution contains continuous data which can
take on any value in range.
Example of Discrete and Continuous data
1. Height of a plant- Continuous data and height is a random continuous (measurable)
variable.
2. How many houses are in a colony? - Discrete data and number of houses is a random
discrete (countable) variable.
Note: when discrete or continuous random numerical data is gathered and each random
numerical variable in data is assigned a probability then we call this a probability distribution
since we now have probability assigned to each variable. Data containing discrete random
numerical variables is called discrete probability distribution and data containing continuous
numerical variables is called continuous probability distribution.
Furthermore, all the probabilities are between zero and one, and the sum of all the probabilities is one
as follows:
0 ≤ P (x) ≤ 1 and ∑ 𝑃(𝑥) = 1 Where P(x) = Probability of random variable x
Where do Probability distributions come from?
Probability distributions come either from empirical data which is based on actual data such as history
or theoretical through mathematical proofs.
Which one is better empirical vs mathematical?
It usually depends on the what is desired result, however, usually empirical data is substituted into
mathematical equations to get better analysis of probability distribution.
Types of Theoretical discrete probability distributions with examples
There are two main types of discrete probability distributions as follows:
i.
Discrete Uniform Distribution:
 It can have n possible values and each value has equal probability i.e., Pi = 1/N e.g.,
rolling a dice.
Fig.1 Shows Probability Mass function graph of discrete uniform distribution (rolling a dice) (Prince 2,
Lecture 10 & 11).
Note: Probability that any of the dice face (from 1 to 6) will show during a dice roll is same i.e., 16 %
ii. Poisson Distribution:
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It is the probability of seeing ‘x’ events within a certain time period e.g., Random arrivals
to a customer service desk.
It is widely used to model arrivals, slow-moving inventory etc.
It is a discrete distribution that cannot take any negative value
It has a notation P(ƛ) where ƛ = 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟 (𝑚𝑒𝑎𝑛)
Probability Mass function formula is:
Where e = Euler’s number 2.718
X! = factorial of X e.g., 7! = 7 x 6 x 5 x 4 x 3x 2 x 1 = 5040
And 0! = 1
Fig.1 Shows Probability Mass function graph of discrete Poisson distribution and it can be scene that
(Prince 2, Lecture 10 & 11)
Note Here X =0 not 1 (as can be seen in tabular form)
Poisson Distribution example numerical
(Prince 2, Lecture 10 & 11)