Probability & Random Variables: Main Points Overview môn Thống kê trong kinh tế và kinh doanh | Trường Đại học Kinh Tế Quốc Dân

Topic ‘Probability and Radom Variables’ Main point list
1. Why do we need probability?
Probability is a fundamental concept in statistics, particularly in the context of probability
theory and random variables, for several important reasons: navigating uncertainty,
making informed decisions, managing risks, and utilizing data effectively.
2. What is a random experiment?
A random experiment is a fundamental concept that refers to a real-world or theoretical
process or event whose outcome is uncertain and governed by chance or randomness. It is
a crucial concept because many statistical analyses and probability calculations are based
on the outcomes of random experiments. It also has different characteristics: uncertainty, repeatability, sample space… 3. What is a sample space?
A sample space refers to the set of all possible outcomes or events that could occur in a
particular business-related situation or experiment. The concept of a sample space is
fundamental for understanding and analyzing uncertainty and randomness in business
processes. The probabilities associated with the outcomes in the sample space help in
assessing risks, optimizing processes, and improving business operations. 4. What is an event?
An event refers to a specific outcome or a combination of outcomes that can occur within
the sample space of a particular business-related situation or experiment. Events are used
to define and describe the different scenarios or possibilities of interest within the context
of business analysis. By defining and analyzing events, businesses can make informed
decisions, manage risks, and optimize processes to achieve their goals.
For example, if you roll a six-sided die, the sample space consists of six possible
outcomes: 1, 2,3, 4, 5, or 6. An event could be rolling an even number, which consists of
the outcomes 2, 4, and6. Another event could be rolling a number greater than 3, which
consists of the outcomes 4, 5, and 6.
5. How many methods are there to measure probability of a single event? List the name.
Classical method: This method is used to calculate the probability of an event
when all the possible outcomes of the experiment are equally likely. The
probability of an event is calculated as the ratio of the number of favorable
outcomes to the total number of possible outcomes.
Relative frequency method: This method is used to estimate the probability of an
event based on the frequency of its occurrence in a large number of trials.
The probability of an event is calculated as the ratio of the number of times
the event occurred to the total number of trials.
Subjective method: This method is used to calculate the probability of
an event based on personal judgment or experience. The probability of
an event is assigned based on the individual's beliefs, opinions, or
subjective assessments of the likelihood of the event occurring
6. List the name of probability of combined events.
There are three types of probabilities of combined events:
Joint Probability: The probability of the intersection of two or more events, denoted as P (A and B).
Marginal Probability: The probability of a single event without considering any
other events, denoted as P (A).
Conditional Probability: The probability of an event given that another event has
occurred, denoted as P (A given B) or P (A|B).
7. What is the purpose of probability tree?
The purpose of a probability tree in business statistics is to help analyze complex decision
scenarios involving uncertainty. It allows businesses to model different choices, assign
probabilities to outcomes, calculate expected values, and identify optimal decisions.
Probability trees are visual tools that aid in risk assessment, strategic planning, and
effective communication of decision-making processes and outcomes.
8. What is the objective of Bayes’ law?
The objective of Bayes' Law in statistics is to update the probability of an event or
hypothesis based on new evidence or information. Bayes' Law, also known as Bayes'
Theorem or Bayes' Rule, is a fundamental principle in probability theory and statistics. It
provides a systematic way to incorporate prior knowledge or beliefs (prior probabilities)
and new data (likelihood) to calculate the revised or posterior probability of an event or hypothesis.
9. What is a random variable (RV)? How many RVs do we have? List the name.
A random variable (RV) is a fundamental concept in probability theory and statistics. It is
a variable that can take on different values, each with a certain probability, depending on
the outcomes of a random experiment or a chance process. Random variables are used to
quantify and model uncertainty and variability in data.
Discrete Random Variable: A discrete random variable is one that can take on a
countable set of distinct values. Each possible value is associated with a
probability of occurrence. Common examples of discrete random variables
include: binominal, poisson, categorical random variables.
Continuous Random Variable: A continuous random variable is one that can take
on any value within a certain range or interval. Instead of probabilities associated
with specific values, we use probability density functions (PDFs) to describe the
likelihood of the variable falling within a particular interval. Common examples
include: normal, exponential, uniform random variables.
Some common examples of random variables include: Binomial random variable Poisson random variable
Normal (Gaussian) random variable Exponential random variable Uniform random variable
10. Which descriptive statistical methods should we use to present univariate probability distribution?
The descriptive statistical methods used to present univariate probability distribution
depend on the type of random variable being analyzed. For a discrete random variable,
we use a probability mass function (PMF), which can be presented using a table or a bar
chart. For a continuous random variable, we use a probability density function (PDF),
which can be presented using a graph such as a histogram or a density plot. Additionally,
we may use measures of central tendency and variability to summarize the distribution of
the random variable. The choice of descriptive statistical methods will depend on the
nature of the random variable and the specificresearch question or problem being addressed.
11. What is the purpose of covariance and correlation coefficient in probability?
Covariance and correlation coefficient are used in probability to measure the strength and
direction of the relationship between two random variables. Covariance measures how
two variables vary together, while correlation coefficient is a standardized version of
covariance, ranging between -1 and +1. They are commonly used in finance, economics,
and psychology to analyze the relationship between variables.