Statistical Distributions

Understanding Statistical Distributions

• Grasping the concept of a statistical distribution and its role in examining variables across a data set.
• Recognising the difference between discrete and continuous distributions and the types of data they describe.
• Understanding the significance of the probability mass function in discrete distributions and the probability density function in continuous distributions.

Discrete Distributions

• Learning about Binomial Distribution and understanding the conditions that need to be met: fixed number of trials, two possible outcomes, and independent events.
• Understanding how the Poisson distribution models events happening at a constant mean rate, independently of the last event.
• Familiarising with the geometric distribution as the model for the number of trials until a specific result is achieved.

Continuous Distributions

• Delving into the Uniform distribution where all outcomes are equally likely within a specified range.
• Understanding the Normal distribution also often called ‘The Bell Curve’ because of its unique bell shape, applicable in many real-world cases.
• Learning about the Exponential distribution, often used to model the time elapsed between events.

Distribution Parameters and Properties

• Recognising the parameters that define specific distributions, such as the mean and standard deviation in a Normal distribution.
• Understanding how the shape and location of a distribution are influenced by these parameters.
• Recognising properties such as kurtosis (tailedness) and skewness (asymmetry) in a distribution.

Central Limit Theorem and Standard Normal Distribution

• Grasping the significance of the Central Limit Theorem, stating that the sum of many independent and identically distributed random variables tends to be normally distributed.
• Understanding Standard Normal Distribution and the utility of Z-scores in standardising random variables for comparison.

Distribution Testing and Model Fitting

• Applying Chi-square goodness-of-fit test to check if an observed distribution fits an expected distribution.
• Gaining knowledge on how to match or ‘fit’ a suitable distribution to a real-world set of data.

Statistical distributions are the foundation of many advanced statistics and data science concepts, hence, a sound understanding of this topic is vital in your mathematical journey. Remember, practising these concepts with a variety of practical examples can greatly enhance understanding and long-term retention.