Lectures "Applied statistics for business - Chapter 5: Discrete probability distributions" provides students with the knowledge: Random variables, developing discrete probability distributions, expected value and variance, expected value and variance financial portfolios,... Invite you to refer to the disclosures.
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Nội dung Text: Lectures Applied statistics for business: Chapter 5 - ThS. Nguyễn Tiến Dũng
- Chapter 5
DISCRETE PROBABILITY DISTRIBUTIONS
Nguyen Tien Dung, MBA
School of Economics and Management
Website: https://sites.google.com/site/nguyentiendungbkhn
Email: dung.nguyentien3@hust.edu.vn
- Main Contents
5.1 Random Variables
5.2 Developing Discrete Probability
Distributions
5.3 Expected Value And Variance
5.4 Bivariate Distributions, Covariance, and
Financial Portfolios
5.5 Binomial Probability Distribution
5.6 Poisson Probability Distribution
5.7 Hypergeometric Probability Distribution
© Nguyễn Tiến Dũng Applied Statistics for Business 2
- 5.1 RANDOM VARIABLES
● A numerical description of the outcome of
an experiment.
● A variable that assume random values,
we don’t know in advance
● Example:
● The upper face of a dice
● The score of customer satisfaction in a
survey
● Time between customer arrivals in minutes
● Two types:
● Discrete
● Continuous
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- A discrete random variable
● A type of random variables that assume a
finite number of values or an infinite sequence
of discrete values
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- Continuous Random Variables
● A random variable that may assume any
numerical value in an interval or collection of
intervals
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- 5.2 DISCRETE PROBABILITY DISTRIBUTIONS
● Required conditions for a discrete f ( x ) 0
probability function:
f ( x ) 1
● Example: the number of automobiles sold
during a day at Dicarlo motors (Table 5.4)
x f(x)
0 0.18
1 0.39
2 0.24
3 0.14
4 0.04
5 0.01
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- Discrete Uniform Probability Function
● f(x) = 1/n
● n = the number of values the random variable may have
● Example:
● x = the number of dots on the upward face of a dice
● x = 1, 2, 3, 4, 5, 6
● f(x) = 1/6
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- 5.3 EXPECTED VALUE AND VARIANCE
● Expected value
E(x)
●𝐸 𝑥 =𝜇= 𝑥𝑓(𝑥)
● Example:
Calculation of the
expected value for
the number of
automobiles sold
during a day at
Dicarlo Motors
● Table 5.5
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- ● Variance
● 𝑉𝑎𝑟 𝑥 = 𝜎 2 = 𝑥 − 𝜇 2 𝑓(𝑥)
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- 5.4 Bivariate Distribution
● A probability distribution involving two random
variables is called a bivariate probability
distribution.
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- A Bivariate Empirical Discrete Probability
Distribution
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- Covariance
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- Correlation Coefficient
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- Financial Applications
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- E(ax+bx) and Var(ax+by)
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- 5.5 BINOMIAL PROBABILITY DISTRIBUTION
● Properties of a binomial experiment
1. The experiment consists of a
sequence of n identical trials.
2. Two outcomes are possible on each
trial. We refer to one outcome as a
success and the other outcome as
a failure.
3. The probability of a success,
denoted by p, does not change from
trial to trial. Consequently, the
probability of a failure, denoted by 1
p, does not change from trial to trial.
4. The trials are independent.
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- Martin Clothing Store Problem:
The Tree Diagram
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