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6.1 Overview: Combining Descriptive
Methods and Probabilities
Slide 1
In this chapter we will construct probability distributions
by presenting possible outcomes along with the relative
frequencies we expect.
6
5
Figure 4-1
6.2 Probability Distribution
Slide 2
™ A random variable is a variable (typically
represented by x) taking numerical values,
determined by outcomes of an experiment
associated with probabilities.
™ A probability distribution is a graph,
table, or formula that gives the
probability for each value of the
random variable.
Example
Slide 3
™ Roll a fair die and observe the number of
dots on the face showing up.
™ Let X= number of dots showing up
= {1, 2, 3, 4, 5, 6} and each value is
associated with a probability of 1/6
™Then the Probability Distribution of X is:
x
1 2 3
1 1 1
P(x)
6 6 6
4 5 6
1 1 1
6 6 6
Definitions
Slide 4
™ A discrete random variable has either a finite
number of values or countable number of
values, where “countable” refers to the fact
that there might be infinitely many values, but
they result from a counting process.
Example: X=the number of TV sets in a household
™ A random variable is not discrete is called
continuous random variable. It takes values
associated with measurements on a
continuous scale in such a way that there are
no gaps or interruptions.
Example: X=a newborn baby’s weight
Graphs
Slide 5
The probability Distribution is very similar to a relative frequency
histogram, but the vertical scale shows probabilities.
Figure 4-3
Requirements for
Probability Distribution
Σ P(x) = 1
Slide 6
where x assumes all possible values
0 ≤ P(x) ≤ 1
for every individual value of x
Mean, Variance and
Standard Deviation of a
Probability Distribution
Slide 7