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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.
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 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