Intro to Probability Distribution

Probability‬
‭

‭outline is on the side‬

‭Histograms and Probability‬
‭➔‬‭the y-axis would represent relative frequency (more continuous) rather than frequency‬
‭➔‬‭area of bars determine the probabilities of the scores‬
‭❗‬ ‭side note‬‭: when calculating joint probability they‬‭should (roughly) add up to 1, and will be‬
‭symmetrical as you near 1 (normal distribution)‬
‭➔‬‭in a binomial distribution, the bars get skinner and closer together and start representing a‬
‭smooth curve (normal distribution)‬

‭Normal Distributions‬
‭➔‬‭distributions can take on many shapes‬
‭◆‬ ‭normal (AKA Guassian distributions)‬
‭◆‬ ‭bimodal‬
‭◆‬ ‭multimodal‬
‭◆‬ ‭unimodal‬
‭◆‬ ‭positively skewed‬
‭◆‬ ‭negatively skewed‬
‭◆‬ ‭leptokurtic‬
‭◆‬ ‭platykurtic‬
‭◆‬ ‭etc.‬
‭➔‬‭a normal distribution is characterized by‬
‭◆‬ ‭mean = median = mode‬
‭●‬ ‭implies symmetry and unimodal‬
‭◆‬ ‭kurtosis = 0‬
‭●‬ ‭nice bell curve shape, not too skinny and not too flat‬
‭◆‬ ‭skew = 0‬
‭●‬ ‭tails are symmetrical on both sides‬
‭➔‬‭what's so special about a normal distribution?‬
‭◆‬ ‭many naturally occurring phenomena are approx. normally distributed‬
‭●‬ ‭no matter how big empirical samples of observations are, they‬‭never will be‬
‭perfectly normal‬‭(even if underlie population is perfectly‬‭normal)‬
‭○‬ ‭as‬‭sample size increases, the shape will reach approximate‬‭normality‬‭but‬
‭never perfect normality‬