Statistics Exam 2 Flashcards
Variables that vary within their domain and depend on the outcome of an experiment.
Random Variables
Type of distribution that has only two outcomes.
Bernoulli Distribution
Defines the “Shape” of a distribution
Parameter
Seeks to determine the probability that something is less than or equal to a number or greater than or equal to a number.
Cumulative Distribution Function (CDF)
The value you would most likely expect for an outcome given a pmf.
Expected Value
Describes the spread of the values of the sample in the population.
Variance of a Random Variable
Applications:
- Tossing of a coin.
- Lights on or off.
- Disease in a person.
- Roulette wheel.
Bernoulli Distribution
Applications:
- The first success occurring on the Xth trial.
- The number of failures before the first success.
Geometric Distribution
The sum of N Bernoulli trials.
Binomial Distribution
Applications:
- Six heads when you toss a coin ten times.
- 12 women in sample size of 20.
- Three defective items in batch of 100.
Binomial Distribution
Applications:
- The Powerball lottery.
- Poker hands.
- Chance of picking a defective part from a box.
- Picking R or D voters in a sample of voters in a district.
Hypergeometric Distribution
Applications:
- Rolling the 5th 6 on the 20th roll of a die.
- Getting the 10th defective item on the 1000th item inspected.
- Selecting the 10th woman as the 15th participant .
Negative Binomial Distribution
Applications:
- Text messages per hour.
- Customers in a restaurant.
- Machine malfunctions.
- Website visitors per month.
Poisson Distribution
Variables that vary within their domain (the sample space), can take on any value in a range, and depend on the outcome of an experiment.
Continuous Random Variables
Distributions that are countable, have distinct points, the points have probability, and p(x) is a probability mass function.
Discrete Distributions
Distributions that are uncountable, are on a continuous interval, the points have no probability, and f(x) is a probability density function.
Continuous Distributions
Applications:
- Random number generator.
- Random sampling.
- Radioactive decay over time.
Uniform Distribution
Applications:
- Heights of individuals.
- Blood pressure.
- IQ scores.
- Measurement errors.
Normal Distribution
Applications:
- Time until a bus arrives.
- Time until the 3rd customer enters.
- Days before travel that a ticket is purchased.
Exponential Distribution
Applications:
- Time between independent events.
- Time until death.
- Time until parts wear out.
- Time until the 3rd accident.
Gamma Distribution
Specifies the number of events you are modeling.
Shape Parameter (Gamma Distribution)
Represents the mean time between events.
Scale Parameter (Gamma Distribution)
Applications:
- Widely used in reliability.
- Fits a wide variety of data sets allowing for both left and right skewed data.
Weibull Distribution
Applications:
- Milk production by cows.
- Lives of industrial units with failure modes.
- Amount of rainfall.
- Size of raindrops.
Lognormal Distribution
Applications:
- Used if there is a finite interval for the RV X.
Beta Distribution
Whether a variation in one variable results in a variation of another.
Covariance
The direction and the strength of the relationship between two variables.
Correlation
Type of probability distribution that is created by drawing many random samples of the given size from the same population.
Sampling
The sampling distribution of the mean will always be normally distributed, as long as the sample size is large enough regardless of the distribution of the underlying population.
Central Limit Theorem
