Probability distributions are key in statistics, outlining how probabilities are assigned to outcomes of random processes. They include discrete distributions, represented by probability mass functions for countable outcomes, and continuous distributions, depicted by probability density functions for uncountable outcomes. The text delves into cumulative distribution functions, uniform distributions, and the binomial probability distribution, highlighting their importance in quantifying uncertainty and modeling random events across various fields.
Show More
Probability distributions assign probabilities to different outcomes of a random process based on the sample space
Discrete Probability Distributions
Discrete probability distributions are used for finite or countable outcomes and require non-negative probabilities that sum to 1
Continuous Probability Distributions
Continuous probability distributions are used for uncountably infinite outcomes and assign probabilities to intervals rather than individual outcomes
CDFs express the probability of a random variable falling within a certain range and are calculated by integrating the probability distribution function
Uniform distributions have equal probabilities for all outcomes within a defined range
Binomial distributions model the number of successes in a fixed number of independent trials with the same probability of success
00
Define Probability Distributions
Probability distributions assign probabilities to outcomes of a random process.
01
Difference: PMF vs PDF
PMF applies to discrete variables, PDF to continuous variables.
02
Example: Fair Die Roll Distribution
Each outcome (1-6) has an equal probability of 1/6.
