All Flashcards
What is the definition of Probability?
The chance of an event occurring.
What is the definition of Random Variables?
Variables whose values are numerical outcomes of random phenomena.
What is the definition of Probability Distributions?
Describe the possible values and likelihoods of a random variable.
What does Independence mean in probability?
One event's outcome doesn't affect another event's outcome.
What does Mutually Exclusive mean in probability?
Events that can't happen at the same time.
What are the differences between Binomial and Geometric Distributions?
Binomial: Fixed number of trials | Geometric: Trials continue until first success
What are the differences between Independent and Mutually Exclusive Events?
Independent: One event doesn't affect the other | Mutually Exclusive: Events cannot occur simultaneously
What are the differences between Categorical and Quantitative Variables?
Categorical: Data falls into distinct categories | Quantitative: Data is numerical and can be measured
What are the differences between binompdf and binomcdf?
binompdf: Calculates the probability of exactly x successes | binomcdf: Calculates the cumulative probability of x or fewer successes
What are the differences between normalcdf and invNorm?
normalcdf: Calculates the probability given z-scores or values | invNorm: Calculates the z-score or value given a probability
What is the formula for Independent Events P(A and B)?
P(A and B) = P(A) * P(B)
What is the formula for Mutually Exclusive Events P(A or B)?
P(A or B) = P(A) + P(B)
What are the conditions (BINS) for Binomial Distribution?
Binary (two outcomes), Independent trials, Number of trials is fixed, Same probability of success for each trial
What is the formula for Z-score?
z = (x - μ) / σ, where x is the observed value, μ is the mean, and σ is the standard deviation.
What is the formula for the expected value of a binomial distribution?
E(X) = np, where n is the number of trials and p is the probability of success.