Chapter 5

Binomial Formula

*insert equation here*

Hypergeometric probability distribution

*insert equation here*

Standard Deviation of a Discrete Random Variable

The standard deviation of a discrete random variable measures the spread of its probability distribution and is computed as

Mean and Standard Deviation of a Binomial Distribution

μ=np and σ=√npq Example μ=np=50(.228)=11.4 σ=√npq=√(50)(.228)(.772)=2.9666

Poisson Probability Distribution Formula

*insert equation here*

Standard Deviation of a Discrete Random Variable Equation

*insert equation here*

Conditions of a binomial experiment

A binomial experiment must satisfy the following four conditions: 1. There are n identical trials. 2. Each trail has only two possible outcomes (or events) 3. The probabilities of the two outcomes (or events) remain constant for each trial. 4. The trials are independent.

Random Variable

A random variable is a variable whose value is determined by the outcome of a random experiment.

Discrete Random Variable

A random variable that assumes countable values is called a discrete random variable.

Continuous Random Variable

A random variable that can assume any value contained in one or more intervals is called a continuous random variable.

Chapter 5

Discrete Random Variables and Their Probability Distributions

Conditions to Apply the Poisson Probability Distribution

The following three conditions must be satisfied to apply the Poisson probability distribution. 1.x is a discrete random variable. 2.The occurrences are random. 3.The occurrences are independent

Mean of a Discrete Random Variable

The mean of a discrete random variable x is the value that is expected to occur per repetition, on average, if an experiment is repeated a large number of times. It is denoted by µ and calculated as: µ=∑xP(x) Example: Table5.6 xP(x) 0(.15) = .00 1(.20) = .20 2(.35) = .70 3(.30) = .90 ΣxP(x) = 1.80 expected value: E(x)=1.80

Probability Distribution of a Discrete Random Variable

The probability distribution of a discrete random variable lists all the possible values that the random variable can assume and their corresponding probabilities.

Two Characteristics of a Probability Distribution

The probability distribution of a discrete random variable possesses the following two characteristics. 1. 0 ≤ P(x) ≤1 2.∑P(x)=1 These two characteristics are also called the two conditions that a probability distribution must satisfy