Application of Mathematical Statistics (0)
Iwona Nowakowska
STATISTICS
Statistical thinking will one day be as necessary for efficient
citizenship as the ability to read and write
H. G. Wells
H. G. Wells (1866 1946)
This English writer and social thinker
Application of Mathematical Statistics (7)
Iwona Nowakowska
Random Variables
In probability and statistics, a random variable is a variable whose value is not
known. Its possible values might represent the possible outcomes of
performed statistical experi
Application of Mathematical Statistics (6)
Iwona Nowakowska
Bernoulli Trials
Jacob Bernoulli (1654 1705)
Two outcomes are possible:
Success or failure
yes / not
Either you make it or you do not.
It happens very often in real life that an event may have o
Application of Mathematical Statistics (8)
Iwona Nowakowska
Discrete Random Variable
continuation
In mathematics, we say that
if the
expected value for the random variable is zero.
Example:
There are two players: A and B. Suppose that they throw a dice.
Applications of Mathematical Statistics
STATISTICAL
 revision
INFERENCE
Applications of M A T H E M A T I C A L S T A T I S T I C S

EXAMPLES
Task 1:
Approximately 1% of women aged 4050 have breast cancer. A woman with breast cancer
has a 90% chance of
Application of Mathematical Statistics (5)
Iwona Nowakowska
Bayes Theorem
Bayes' theorem (also known as Bayes' rule) is a useful tool for calculating
conditional probabilities.
Theorem:
Bayes Theorem
Thomas Bayes (17011761)
If the conditions are held:
1
Application of Mathematical Statistics (9)
Iwona Nowakowska
Random Variables
Continuous random variable
Notation:
random variable
for a continuous random variable
is defined by the function , which is called probability density
function, for which two f
Application of Mathematical Statistics (3)
Iwona Nowakowska
Dependence and independence of the events
In probability theory, to say that two events are independent intuitively means
that the occurrence of one event makes it neither more nor less probable
Application of Mathematical Statistics (4)
Iwona Nowakowska
Total Probability Theorem
(Law of total probability)
The law of total probability is a fundamental rule relating to conditional
probabilities.
Theorem:
Law of total probability
If the conditions
Case Study
1 a. Obtain the financial information you need for Home Depot, get the current stock price and number of shares o
Stock Price/ USD
143
1,218,160,970
Shares Outstanding
c. Select the latest yield on an outstanding bond with the shortest
remaini
Problem 1
Problem 2
Property type
Office building
Property size
200,000 square feet
Gross rental income
25 per square foot
Other income
75.00
Vacancy and collection loss 5% of potential gross income
Property taxes and insurance
350.00
Utilities and main