BIOM301 Chapter 5 Discrete Probability Distribution Random Variables A variable x whose value depends on the outcome of a chance operation o 1 outcome per run of the chance operation o Every outcome is independent of every other outcome Two main groups o Discrete Random Variables Chapter 5 quantitative discrete o Continuous Random Variables Chapter 6 quantitative continuous Discrete Random Variables Probability Function P x Distribution or Histogram o Show all possible mutually exclusive outcomes ALL POSSIBLE OUTCOMES THAT COULD OCCUR o Sum of all event probabilities equal to 1 Can compare the likelihood of one event to another Probability Distributions represent theoretical populations o We can calculate Population Parameters the spread The mean u is viewed as the expected value Binomial Variables variables that can only have 2 possible outcomes o All binomial variables are discrete variables but not all discrete variables are not binomial variables Ex Gender male or female or Coin toss head or tails o Often can flip any variable into a binomial perspective Discrete of eggs in a nest Binomial With eggs or without eggs o Can also flip non discrete variables into a binomial perspective Eggs in Nests T shirt Size Ordinal small medium and large Binomial small vs not small Binomial Probability Distribution Based on a series of repeated trials whose outcomes fall into either success or failure o Need to consider ALL ways you can get a certain outcome o We ASSUME that all observations are independent and that the data results from chance events Binomial Coefficient of ways that exactly x successes can occur in n trials If we know P success we can generate the EXPECTED distribution of outcomes Rare Events unusual Any time that probability of some event is less than 5 it suggests the event may be rare or Predicting the Shape of the Binomial Probability Distribution Need to know n and p We can then calculate the mean and the variance Increase p graph move to the right Decrease p graph moves to the left Increase n the graph becomes more symmetric normal less skewed Chi Square Goodness of Fit Test Statistical test to ask if your observed values MATCH to what your expected IF your data follow some distribution o Can use for check fit of binomial data o Can also use any time you have a prediction of how data are distributed
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