CH7: Random Variables and Discrete Probability Distributions

Poisson Experiment; E(X)=V(X)=λ.

an experiment that counts the number of successes in a given time or space, staying independent and constant

Bivariate Distribution P(x,y)

Probability of the combination of two events

Continuous Random Variable

random variable with infinite amount of values

Binomial Experiment

fixed number of trials with two outcomes, where the probability of each outcome is constant for every trial.

Cumulative Probability

probability that a random variable is less than or equal to a specific value

Expected Value

population mean

Binomial Random Variable

The number of successes occurring in the n trials of a binomial experiment

Discrete Random Variable

random variable with finite amount of values

Binomial Experiment Requirements

fixed # of trials, two possible outcomes per trial, constant probability per trial, independent

Binomial E(x)=?

np

Binomial V(x)=?

np(1-p)

Uniform Distribution

All outcomes are equally likely within a specific range

Normal Distribution

A bell-shaped curve where most values are close to the mean

Standard Normal Distribution: Z∼N(0,1).

A normal distribution with a mean of 0 and standard deviation of 1

Random Variable

Normal Distribution Properties

Symmetric, mean = median = mode

Marginal Probability

probability of one variable in a bivariate distribution, ignoring the other

Conditional Probability

probability of one event given that another event has occurred.