Statistics 528  Lecture 16
1
Statistics 528  Lecture 16
Prof. Kate Calder
1
Continuous Random Variables
Assigning Probabilities to Infinite Sample Spaces
Consider the random variable X representing the weight you gained in the
last month. What are the possible values that X can take?
=>
there are infinite number of values
•
X is a
continuous random variable
(takes values in an interval of
numbers)
Statistics 528  Lecture 16
Prof. Kate Calder
2
•
How can we assign probabilities to events such as {1 < X < 3}?
•
It is not possible to count the total number of outcomes that make up
this event and add their probabilities because there are too many (an
infinite number of) possible outcomes.
•
We use another way of assigning probabilities to the intervals of
outcomes like the above – use areas under the density curves.
The
probability distribution
of X is described by a density curve.
The probability of any event is the
area under the density curve
above
the values of X that make up the event.
Statistics 528  Lecture 16
Prof. Kate Calder
3
Recall density curves from the chapter 1:
•
The total area under the curve is 1 and the curve always falls on or
above the xaxis.
•
The area under a density curve in any given range of values (interval)
gives the proportion of observations that fall in that range. We assign
this proportion as the probability of observing an outcome in that
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 Winter '09
 Calder
 Probability theory, probability density function, Prof. Kate Calder

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