Discrete and Continuous Random Variables

These flashcards cover key concepts related to discrete and continuous random variables, probability distributions, transformations, binomial and geometric distributions, and related conditions for inference.

Discrete Random Variable

A variable that takes a countable number of values with gaps between.

Continuous Random Variable

A variable that has an infinite number of values with no gaps.

Probability Distribution

A mathematical function that provides the probabilities of occurrence of different possible outcomes.

Mean (Expected Value)

The average or expected value calculated as Mx=Σxi*P(x).

Variability of a Random Variable

A measure of how much the values of a random variable differ from the mean, calculated as O√(x-M)P(x).

Uniform Distribution

A type of continuous probability distribution where all outcomes are equally likely.

Normal Distribution

A continuous probability distribution characterized by its bell-shaped curve, defined by its mean and standard deviation.

Binomial Random Variable

A random variable that counts the number of successes in a fixed number of independent trials, each with the same probability of success.

Binomial Distribution Formula

The formula P(x=k) = nk * P^k * (1-p)^(n-k) used to calculate probabilities in a binomial distribution.

Geometric Distribution

A distribution that models the number of trials until the first success, with trials being independent and binary.

10% Condition

A condition stating that in a binomial distribution, for sampling without replacement, n should be less than or equal to 10% of the population size N.

Large Counts Condition

A condition stating that a binomial distribution can be approximated by a normal distribution if np≥10 and n(1-p)≥10.

Transforming Random Variables

The process of adding or subtracting constants or multiplying or dividing by constants, affecting the center and variability.