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Chapter 8: Discrete Probability Distributions
327
Thus, the standard deviation for a random variable
X
, denoted by
, is given
below.
Note:
The variance and the standard deviation for a probability distribution is
equal to its population variance and standard deviation respectively.
Example 8-9
:
What is the standard deviation of the winnings for a raffle
with a first prize of $1000, a second prize of $500, and a third prize of $300
if 1,000 tickets are sold given in
Example 8-6
?
Solution:
If we let the winnings for the raffle be represented by the
random variable
X
, then recall that
=
V
(
X
) = 1336.76. Hence the standard
deviation
=
SD
(
X
) =
√
= 36.56.
Note:
The unit for the standard deviation here will be dollars ($) so
=
$36.56.
Observe from
Figure 8-11
that the standard deviation is also computed by
the workbook. It displays a value of 36.5617 (to four decimal places) for
this example.
Example 8-10
:
Find the standard deviation for the profits in the two
portfolios in
Example 8-8
.
Solution:
Let the profit for portfolio A be represented by the random
variable
X
, and let the profit for portfolio B be represented by the random
variable
Y
.
Then,
= SD(
X
) =
√
= 1048.9995 (to four decimal places).
= SD(
Y
) =
√
= 1772.1174 (to four decimal places).