Discrete Probability Distributions Tutorial Sheet - STEP BY STEP SOLUTIONS
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PMF vs. PDF Definitions
The Probability Mass Function (PMF) defines the probability of a discrete random variable taking a specific value, with key characteristics that probabilities are non-negative and sum to one. The Probability Density Function (PDF) describes the likelihood of a continuous random variable falling within an interval, where probabilities are non-negative and the integral over the entire range is one. A key difference is that PMF gives probability at exact values, while PDF gives probability over intervals.
Discrete Random Variable Definition
A discrete random variable is defined as a variable that can take on a finite or countably infinite set of values. Examples include the number of students in a class or the number of heads in a series of coin tosses. This contrasts with continuous random variables that can assume any value within an interval.
Poisson Distribution Definition and Characteristics
The Poisson distribution is a discrete distribution modeling the number of events in a fixed interval of time or space, provided events occur independently and at a constant average rate (lambda). Key characteristics include events occurring one at a time, independence, a constant average rate, and negligible probability of multiple events in very short intervals. Its PMF formula involves 'e', lambda, and 'k'.
