Probabilidad Básica

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.

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.