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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.
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.
Explain the concept of Normal Distribution.
Bell-shaped and symmetrical, used to model many real-world phenomena. Characterized by mean (μ) and standard deviation (σ).
Explain the concept of Binomial Distribution.
Used for a fixed number of independent trials with two outcomes (success or failure).
Explain the concept of Geometric Distribution.
The number of trials needed until the first success.
Explain the concept of z-scores.
Measure how many standard deviations a value is from the mean in a normal distribution.
Explain the concept of density curves.
The area under a density curve represents probability.