Untitled Flashcards Set

Random Variables

Numerical values that describe the outcomes of a random process.

Discrete Random Variables

Variables that take a countable set of possible values with gaps between them.

Continuous Random Variables

Variables that can take any value within a given range.

Expected Value

The long-run average value of a random variable after many trials, denoted by 𝜇x or E(X).

Standard Deviation

A measure of the spread of a probability; indicates how far data points deviate from the mean.

Variance

Standard deviation squared; mathematically convenient for calculations.

Geometric Distribution

Describes the number of trials needed to achieve the first success in a series of independent trials.

Cumulative Distribution Function (CDF)

Calculates the probability that a random variable will take on a value less than or equal to a specific value.

Probability Density Function (PDF)

Represents the probability of a continuous random variable taking on a specific value within a given range.

Binomial Distribution

Describes the probability of obtaining a specific number of successes in a fixed number of independent trials.

Mean of Random Variables

Calculated by adding the values of the random variable and dividing by the number of trials.

Mean of a Binomial Distribution

Calculated using the formula n*p where n is the number of trials and p is the probability of success.

Mean of a Geometric Distribution

Calculated using the formula 1/p where p is the probability of success.

Normal Approximation to Binomial

Used when np > 10 and n(1-p) > 10.

Transforming Random Variables

Adding a constant affects measures of center; multiplying affects both measures of center and spread.