What is normal and poisson distribution? What is the difference between them?

Question Analysis

This question is asking you to explain two fundamental statistical distributions: the normal distribution and the Poisson distribution. You need to describe each distribution's characteristics, applications, and the differences between them. Understanding both distributions is crucial as they are commonly used in data analysis to model different types of data. You should focus on their properties, such as shape, parameters, and usage scenarios.

Answer

Normal Distribution:

• Description: The normal distribution, also known as the Gaussian distribution, is a continuous probability distribution characterized by its bell-shaped curve.
• Properties:
  • Symmetrical: The distribution is symmetric around its mean.
  • Parameters: It is defined by two parameters: the mean (μ) and the standard deviation (σ).
  • 68-95-99.7 Rule: Approximately 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three.
• Applications: Commonly used in natural and social sciences to represent real-valued random variables whose distributions are not known.

Poisson Distribution:

• Description: The 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.
• Properties:
  • Parameters: Defined by a single parameter λ (lambda), which is the average number of events in the interval.
  • Discrete: It deals with events that occur at a certain rate but independently of the time since the last event.
• Applications: Often used to model count data and rare events, such as the number of phone calls received by a call center or the number of decay events per unit time from a radioactive source.

Differences:

• Type: Normal distribution is continuous, while Poisson distribution is discrete.
• Parameters: Normal distribution uses mean and standard deviation, while Poisson uses only the rate (λ).
• Shape: Normal has a symmetrical bell shape, whereas Poisson is typically skewed unless λ is large, at which point it begins to resemble a normal distribution.

By understanding these differences and characteristics, you can apply the appropriate distribution model to your data analysis tasks effectively.