Statistics and Probability Dictionary
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Continuous Probability Distribution
If a random variable
is called a
A continuous probability distribution differs from a discrete probability
distribution in several ways.
The probability that a continuous random variable will assume a particular
value is zero.
As a result, a continuous probability distribution cannot be expressed in
Instead, an equation or formula is used to describe a continuous probability
The equation used to describe a continuous probability distribution is
called a probability density function (pdf).
All probability density functions satisfy the following
- The random variable Y is a function of X; that is, y = f(x).
The value of y is greater than or equal to zero for all
values of x.
- The total area under the curve of the function is equal to one.
The charts below show two continuous probability distributions.
The first chart shows a probability density function
described by the equation y = 1 over the range of 0 to 1 and y = 0
|y = 1
The next chart shows a probability density function
described by the equation y = 1 - 0.5x over the range of 0 to 2 and y = 0
elsewhere. The area under the curve is equal to 1 for
|y = 1 - 0.5x
The probability that a continuous random variable falls in the
interval between a and b is equal to the
area under the pdf curve between a and b.
For example, in the first chart above, the shaded area shows
the probability that the random variable X will
fall between 0.6 and 1.0. That probability is 0.40.
And in the second chart, the shaded area shows
the probability of falling between 1.0 and 2.0.
That probability is 0.25.