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Title: Random Variables
Description: These notes detail different symbols used to represent random variables, as well as how to define and identify random variables in a data set. These are college level notes but they can also be used for high school classes and AP courses.
Description: These notes detail different symbols used to represent random variables, as well as how to define and identify random variables in a data set. These are college level notes but they can also be used for high school classes and AP courses.
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Random Variables
Saturday, April 2, 2016
6:28 PM
Two Types of Random Variables
•
A random variable assumes numerical values associated with the random
outcomes of an experiment, where one (and only one) numerical value is
assigned to each sample point
• Random variables that can assume a countable number (finite or infinite) of
values are called discreet
○ Number of
...
e
...
Then, depending on the shape of p(x), the following
of the variance
○ Sigma = sqrt(sigma^2) = sqrt(SUM(x - µ)^2)*SUM p(x)
Probability Rules for a Discrete Random Variable
Let x be a discrete random variable with the probability distribution p(x), mean µ, and
standard deviation sigma
...
68
P(µ - 2sigma < x < µ + 2sigma)
>/= 3/4
About
...
We will denote one
outcome by S (for success) and the other by F (for failure)
○ The probability of S remains the same from trial to trial
...
§ Q = 1 - p
○ The trials are independent
○ The binomial random variable x is the number of S's in n trials
The Binomial Probability Distribution
P(x) = (n over x)(p^x)*(q^n -x)
P = probability of success on a single trial
Q = 1 - p
N = number of trials
X = number of successes in n trials (0, 1, 2,
...
)
• Mean µ = l
• Variance sigma^2 = l
• The hypergeometric probability distribution provides a realistic model for some
types of enumerative (countable) data
○ The experiment consists of randomly drawing n elements without
replacement from a set of N elements, r of which are S's (for success) and
(N - r) of which are F's (for failures)
○ The hypergeometric random variable x is the number of S's in the draw of
n elements
• Hypergeometric trials are dependent, while the binomial trials are independent
• Probability distribution p(x) = (r over x)(N - r over n - x)/(N over n) where x =
maximum[0, n - (N -r)],
Title: Random Variables
Description: These notes detail different symbols used to represent random variables, as well as how to define and identify random variables in a data set. These are college level notes but they can also be used for high school classes and AP courses.
Description: These notes detail different symbols used to represent random variables, as well as how to define and identify random variables in a data set. These are college level notes but they can also be used for high school classes and AP courses.