뒤로Introduction to Probability in Statistics
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Introduction to Probability
Formulating Hypotheses and Experiments
In statistics, we often aim to make claims or hypotheses about a certain situation. To do this, we set up a gathering process, called a procedure, to collect data and determine if the results support our claim.
Simple event: An event that cannot be broken down into smaller events.
Sample space: The set of all possible outcomes of an experiment.
Example: Tossing a coin is a simple event. The sample space for tossing a coin is {Heads, Tails}.
Events and Sample Spaces
Simple Event: For 1 coin flip, the sample space is {H, T}.
Full Event: For 3 coin flips, the sample space is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.
Number of Outcomes: For n coin flips, the number of possible outcomes is .
Example: If you flip a coin 3 times, there are possible outcomes.
Probability Concepts
Definition of Probability
Probability is the likelihood of an event occurring. It is denoted as , where A is the event.
General Form:
Success: The outcome we are interested in or are "shooting for".
Probability as a Decimal or Fraction: Probability is expressed as a number between 0 and 1.
Probability Range:
Interpretation:
: The event is impossible.
: The event is certain to happen.
Types of Probability Measures
There are three major types of probability measures:
Classical Probability: Used in closed systems where all outcomes are known (e.g., games, simple events).
Formula:
Relative (Frequency) Probability: Based on observation of the event and counting outcomes in the real world.
Comparison Table: Types of Probability
Type | Description | Example |
|---|---|---|
Classical Probability | All outcomes are known and equally likely | Rolling a fair die |
Relative (Frequency) Probability | Based on observed frequencies in real-world experiments | Counting how often it rains in a month |
Additional info: Subjective Probability | Based on personal judgment or experience | Estimating the chance of a team winning a game |
Key Terms and Concepts
Event: A specific outcome or set of outcomes from an experiment.
Sample Space: The set of all possible outcomes.
Probability: A measure of how likely an event is to occur.
Success: The outcome of interest in a probability experiment.
Example Calculation
Example: What is the probability of getting exactly two heads in three coin flips?
Possible outcomes: {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Outcomes with exactly two heads: HHT, HTH, THH (3 outcomes)
Total outcomes: 8
Probability:
Additional info: Subjective probability is sometimes included as a third type, based on personal belief or experience, but is less formal than classical or relative probability.
