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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
What is the formula for calculating binomial probability P(X = x)?
$P(X = x) = \binom{n}{x} * p^x * (1-p)^{(n-x)}$
What does 'n' represent in the binomial probability formula?
n = number of trials
What does 'p' represent in the binomial probability formula?
p = probability of success on a single trial
What does 'x' represent in the binomial probability formula?
x = number of successes
What is the formula for the standard deviation of a binomial distribution?
$\sqrt{np(1-p)}$
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 $\binom{n}{x}$ or nCx.