Stats 126 CH 6 (6.1-6.3)

random variable

a numerical measure of the outcome from a probability experiment, so its value is determined by chance. Denoted by variables like X.

discrete random variable

either a finite or countable number of values. can be plotted on a number line with space between each point.

continuous random variable

has infinitely many values. can be plotted on a line in an uninterrupted fashion

probability distribution

a discrete random variable X provides the possible values of the random variable and their corresponding probabilities. Can be in the form of a table, graph, or formula

Rules for a discrete probability distribution

1. summation P(x)=1

2. 0 less than or equal to P(X) less than or equal to 1

interpretation of the mean of a discrete random variable

as the sample size increase the closer the difference between x-bar and mu gets closer to zero.

expected value

another name for the mean of a random variable

binomial probability distribution

a discrete probability distribution that describes probabilities for experiments in which there are two mutually exclusive (disjoint) outcomes.

• outcomes are referred to as success and failure

binomial experiments

experiments where only 2 outcomes are possible (success or failure)

Criteria for a binomial probability experiment

1. the experiment is performed a fixed number of times (repetitions are called trials)

2. trials are independent

3. each trial has two disjoint outcomes, success or failure

4. probability of success is fixed for each trial of the experiment

binomial random variable

the random variable X is the number of successes in n trials of a binomial experiment.

notation used in binomial probability distribution

1. n= independent trials of experiment

2. p= probability of success and 1-p= probability of failure

3. X= number of successes in n independent trials of the experiment so, 0<x<n

poisson process

1. probability of two or more successes in any sufficiently small subinterval is 0

2. the probability of success is the same for any two intervals of equal length

3. the number of successes in any interval is independent of the number of successes in any other interval provided the intervals are not overlapping

at least and more than probabilities for a Poisson process

these probabilities must be found using the complement rule since the random variable X can be any integer greater than or equal to 0