All Flashcards
What is a probability distribution?
A map of possible outcomes for a random event, indicating the likelihood of each outcome.
What is a binomial random variable?
Counts the number of successes in a fixed number of independent trials.
Define 'success' in a binomial setting.
One of the two possible outcomes in each trial of a binomial experiment.
Define 'failure' in a binomial setting.
The other one of the two possible outcomes in each trial of a binomial experiment, that is not the 'success'.
What does the binomial coefficient represent?
The number of ways to choose x successes from n trials, denoted as or nCx.
What are the differences between binomPDF and binomCDF?
binomPDF: Probability of exactly x successes | binomCDF: Probability of x or fewer successes
What are the differences between theoretical and empirical probability?
Theoretical: Uses rules of probability | Empirical: Uses observed frequencies from simulations
What are the differences between binomial and geometric distributions?
Binomial: Fixed number of trials | Geometric: Number of trials until the first success
What are the differences between success and failure in a binomial trial?
Success: The outcome of interest | Failure: Any outcome that is not the outcome of interest
What are the differences between independent and dependent trials?
Independent: Outcome of one trial doesn't affect others | Dependent: Outcome of one trial affects others
Explain the concept of independent trials in a binomial setting.
The outcome of one trial does not influence the outcome of any other trial.
Explain the purpose of binomPDF.
binomPDF calculates the probability of exactly x successes in n trials.
Explain the purpose of binomCDF.
binomCDF calculates the probability of x or fewer successes in n trials.
What are the conditions (BINS) for a binomial setting?
Binary (Success/Failure), Independent, Number of trials is fixed, Same probability of success.
Why is it important to interpret binomial probabilities in context?
Interpreting in context provides meaning to the numerical result and is often required for full credit on assessments.