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4-1 Continuous Random Variables
A continuous random variable is one that can take any value in an interval of the real
number line.
OR
A continuous random variable is a random variable where the data can take infinitely many
values.
For example, a r

3-6 Binomial Distribution
Binomial Experiment:
A binomial experiment (also known as a Bernoulli trial) is a statistical
experiment that has the following properties:
The experiment consists of n repeated trials.
Each trial can result in just two possibl

4-8 Exponential Distribution
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4-8 Exponential Distribution
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4-8 Exponential Distribution
The following have an EXPONENTIAL DISTRIBUTION:
the time until the first event
the time from now until the next occurrence of an event
the time interval between

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3-1 Discrete Random Variables
A random variable is a variable whose value is a numerical outcome
of a random phenomenon.
A random variable is denoted with a capital letter such as X, Y
The probability distribution of a random variable X tells what
the

5-3 COMMON JOINT DISTRIBUTIONS
5-3.1 Multinomial Probability Distribution
Multinomial Experiment
A multinomial experiment is a statistical experiment that has the
following properties:
The experiment consists of n repeated trials.
Each trial has a discr

2-4 Conditional Probability
The conditional probability of an event B, in relation to event A, is the probability
that event B will occur given the knowledge that an event A has already occurred.
In plain English .
You toss two pennies. The first penny sh

2-2 Interpretations of Probability
2-2.1 Introduction
Probability
Used to quantify likelihood or chance
Used to represent risk or uncertainty in engineering
applications
Can be interpreted as our degree of belief or relative
frequency
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2-2 Interpretat

4-6 Normal Distribution
The normal or Gaussian distribution, named for German
mathematician Karl Gauss (17771855)
The normal distribution is the most important and widely used
distribution in statistics.
The bell-shaped curve explains many natural pheno

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5-1 TWO OR MORE RANDOM VARIABLES
5-1.1 Joint Probability Distributions
Joint probability density function (PDF) is a function of two or more random
vaiables X and Y or more.
If X and Y are discrete random variables, the joint probability distribut

3-7 Geometric and Negative Binomial
Distributions
Geometric Distribution
Consider a random experiment that is closely related to the one
used in the definition of a binomial distribution.
Assume a series of Bernoulli trials (independent trials with cons