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About this document
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- 38 pages
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- $38 one-time, yours to keep
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- Subject
- Mathematics, Statistics
This document explains probability in everyday life, and introduces random experiments, sample space, events, and types of events. It is useful for understanding basic probability concepts.
What's inside
- Probability in everyday life
- Random experiments and sample space
- Events and their occurrence
- Types of events
- Algebra of events
- Mutually exclusive and exhaustive events
Who it is for: For students learning about probability and statistics. (Undergraduate)
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Summary
Probability is a branch of mathematics that studies uncertain events. It is used in everyday life and in games of chance. It explains how to measure the chance of events happening.
Probability in daily life
Probability is used to make decisions based on uncertain events. Examples include weather forecasts and health statements. People have always been interested in games of chance. The study of probability began in the fifteenth century.
Random experiments and sample space
A random experiment is one where the outcome cannot be predicted in advance. The set of all possible outcomes is called the sample space. Each possible outcome is a sample point.
Events and their occurrence
An event is an outcome or a combination of outcomes of an experiment. Events can be mutually exclusive or exhaustive. The occurrence of one event can affect the occurrence of another.
Random variables and their distribution
A random variable is a function that assigns a real number to each element in the sample space. It can be discrete or continuous. The probability distribution of a random variable shows the probabilities of its possible values.
Key terms
- Random experiment
- An experiment where the outcome is uncertain and can be one of several possible outcomes.
- Sample space
- The set of all possible outcomes of a random experiment.
- Event
- An outcome or a combination of outcomes of an experiment.
- Random variable
- A function that assigns a real number to each element in the sample space.
- Mutually exclusive events
- Events that cannot occur at the same time.
- Poisson distribution
- A probability distribution that can be used as an approximation to the binomial distribution when n is large and p is small.
Questions this document helps with
- How do you measure the chance of an event happening?
- What is the difference between a deterministic and a random experiment?
- When are two events said to be mutually exclusive?
Summary written with AI from the document's text.
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