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Lecture 5:
CHAPTER 2: PROBABILITY
Random Variables (Section 2.4, page 88)
Definition:
A numerical characteristic whose value depends on the outcome of a
chance experiment is called a
random variable
.
A random variable
is
discrete
if its possible values form a finite set or, perhaps, an
infinite sequence of real numbers.
Otherwise, a variable is
continuous
if its possible values span an entire interval of real
numbers.
We have already learned about discrete data and continuous
data….now let’s extend this to random variables.
Example of a random variable:
The measured yield of a chemical reaction.
There can be any number of random variables associated with a
chance experiment.
In a chemical reaction, any quantifiable feature
associated with a chance experiment is a random variable (e.g., yield,
density, weight, and volume of the material produced.)
We denote random variables by letters, for example:
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Example:
Computer chips often contain surface imperfections.
For
a certain type of computer chip, 9% contain no imperfections, 22%
contain 1 imperfection, 26% contain 2 imperfections, 20% contain 3
imperfections, 12% contain 4 imperfections, and the remaining 11%
contain 5 imperfections.
Let Y represent the number of imperfections
in a randomly chosen chip.
What are the possible values for Y?
Is Y
discrete or continuous?
Find P(Y=y) for each possible value y.
Probability Distributions
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 Winter '11
 Paula
 Probability, 9%, 12%, 11%, 0.8 mm, 5lb

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