Econ 180. Assignment 4.
Continuous Random Variables: Normal Distribution.
1.
Def:
The continuous probability distribution
is the probability distribution of a continuous random
variables (X).
It can not be presented in
tabular
form, but it can be presented by a formula.
Such a
formula
would necessarily be a function of the numerical values of the continuous variable X as such
could be graphed as a
smooth curve
.
The probability function portrayed by this curve is called
probability density function (pdf), a frequency distribution, or a probability distribution.
2.
Def:
Probability density function
(pdf): Let X be a continuous random variable, and x be any lying in
the range of values this random variable can take.
pdf, f(x) of the random variable is a function with
the following properties:
∞
(1) The area under its curve and above the x axis is equal to 1, i.e., ⌠
f(x)dx = 1.
∞.
(2) The area under the curve between two ordinates x = a and x = b with a < b gives the probability that
x lies between a and b, i.e., p(a ≤ x ≤ b) = p(a < x < b).
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 '10
 Shieh,YeungNan
 Normal Distribution, Probability distribution, Probability theory, probability density function, Continuous probability distribution

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