Probabilidad Básica

Study Notes

Probability

Probability is the measure of the likelihood of an event occurring.
It's expressed as a number between 0 and 1, inclusive.
0 indicates impossibility, 1 indicates certainty.
A probability of 0.5 represents an equal chance of the event happening or not.
Probability is often calculated using ratios of favorable outcomes to total possible outcomes.

Basic Probability Rules

Complement rule: The probability of an event not occurring is 1 minus the probability of it occurring.
Addition rule: For mutually exclusive events, the probability of either event occurring is the sum of their individual probabilities.
Multiplication rule: For independent events, the probability of both events occurring is the product of their individual probabilities.

Types of Probability

Theoretical probability: Calculated using the ratio favorable outcomes/total possible outcomes (provided knowledge is complete).
Empirical probability: Calculated by performing repeated experiments, observing frequencies, and calculating relative frequencies.
Subjective probability: Based on an individual's judgment or opinion.

Random Variables

A random variable is a variable whose value is a numerical outcome of a random phenomenon.
Discrete random variables: Can only take on specific values (e.g., integers).
Continuous random variables: Can take on any value within a given interval.

Expected Value

The expected value of a random variable is the weighted average of all possible values, weighted by their probabilities.
Represents the average outcome over many trials.
It's calculated by summing the products of each value and its probability.

Statistical Inference

Uses sample data to draw conclusions about a population.
Involves using sample statistics to estimate population parameters.
Provides a framework to validate and evaluate theories by observing and analyzing collected data.

Descriptive Statistics

Summarizes and describes data.
Measures of central tendency: Mean, median, mode.
Measures of dispersion or variability: Range, variance, standard deviation.
Frequency distributions: Show how data points are distributed across different categories.

Inferential Statistics

Draw inferences and conclusions from a sample about the population it represents.
Includes hypothesis testing and confidence intervals.
Allows to quantify the uncertainty associated with conclusions.
Crucial in making decisions based on limited data.

Distributions

Normal distribution: A bell-shaped, symmetrical probability distribution.
Binomial distribution: Describes the probability of getting a certain number of successes in a fixed number of independent Bernoulli trials.
Poisson distribution: Describes the probability of a given number of events occurring in a fixed interval.

Hypothesis Testing

A process to determine whether there is enough evidence to reject a null hypothesis in favor of an alternative hypothesis.
Null Hypothesis (H0): A statement of no effect or no difference.
Alternative Hypothesis (Ha): A statement contradicting the null hypothesis.
Steps involved include defining hypotheses, selecting a significance level, calculating a test statistic, and making a decision.

Description

Este cuestionario trata sobre la probabilidad y sus reglas básicas. Aprenderás acerca de la probabilidad teórica y empírica, así como las reglas de complemento, adición y multiplicación. Ideal para estudiantes que quieren aprofundizar en conceptos de probabilidad.