Lec 09 –Continuous Random Variables
IOE 265 F11
1
1
Continuous Random
Variables
2
Topics
I.
Continuous Random variables
II.
Probability distributions for continuous
random variables
III.
Expected values of continuous random
variables

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Lec 09 –Continuous Random Variables
IOE 265 F11
2
3
I. Continuous Random Variables
Definition: A random variable (rv) X is said to
be continuous if its set of possible values is
an entire interval of numbers.
Example: suppose
X
is an rv representing all
values for a diameter between 15 and 20 mm.
Or, X could be defined as 15 <= X <= 20
4
Continuous
Vs. Discrete
Key issue: if units for X can be subdivided to
any
extent
continuous; if not
discrete
Money - ?
Height – ?
Practical uses –
Although many continuous variables have limitations in the
extent in which they may be measured (precision of measuring
instrument), we prefer to treat them as continuous.
Similarly, some discrete variables also may be treated as
continuous.
Why?
continuous variables often are easier to manipulate.