Continuous Random Variable
Submitted by gfj100 on Wed, 11/11/2009  10:42
Density Curves
Previously we discussed discrete random variables, and now we consider the contuous type.
A
continuous random variable
is such that all values (to any number of decimal places) within
some interval are possible outcomes. A continuous random variable has an infinite number of
possible values so we can't assign probabilities to each specific value. If we did, the total
probability would be infinite, rather than 1, as it is supposed to be
To describe probabilities for a continuous random variable, we use a
probability density
function.
A
probability density function
is a curve such that the area under the curve within any
interval of values along the horizontal gives the probability for that interval.
Normal Random Variables
The most commonly encountered type of continuous random variable is a
normal random
variable
, which has a symmetric bellshaped density function. The center point of the
distribution is the mean value, denoted by μ (pronounced "mew"). The spread of the distribution
is determined by the variance, denoted by σ
2
(pronounced "sigma squared") or by the square root
of the variance called standard deviation, denoted by σ (pronounced "sigma").
Example
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 Spring '11
 AndyRegards
 Normal Distribution, Probability, Probability theory, probability density function

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