Outline Chapter 3: Random Sampling, Probability, and the Binomial Distribution Part II
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Density Curves
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Random Variables
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The Binomial Distribution
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Fitting a Binomial Distribution to Data
Eric D. Nordmoe Math 261 Department of Mathematics and Computer Science Kalamazoo College
Spring 2009
Random Sampling Model
Random Variables A random variable is a variable that takes on numerical values that depend on the outcome of a chance operation.
Probability Model
Types of Random Variables
Random Sampling
Population
Sample
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Continuous random variables take values on a continuous scale.
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Discrete random variables have a discrete list of possible values.
Probability Models for Random Variables
Density Curve Example
The method of characterizing the distribution of a random variable depends on the nature of the variable:
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The distribution of a continuous random variable is described by a density curve. I
A probability density may be viewed as an idealized histogram.
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Continuous Random Variables
Density
The distribution of a discrete random variable is described by the probability distribution comprised of enumerated possible values and corresponding probabilities.
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Discrete Random Variables
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A stylistic example
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Diastolic Blood Pressure
Histogram Density Curve
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The proportion of the distribution that falls in that range. The probability that a randomly selected individual has a value in that range.
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The total area underneath the density is 1. The area under the curve and above any range of values can be interpreted in two ways:
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The density curve always lies on or above the horizontal axis.
