Probability And Statistics Applications Study Cards

Enhance Your Learning with Probability and Statistics Flash Cards for quick revision



Probability

The measure of the likelihood that an event will occur.

Sample Space

The set of all possible outcomes of an experiment.

Random Variable

A variable that can take on different values based on the outcome of a random event.

Probability Distribution

A function that describes the likelihood of different outcomes in a sample space.

Binomial Distribution

A discrete probability distribution that models the number of successes in a fixed number of independent Bernoulli trials.

Normal Distribution

A continuous probability distribution that is symmetric and bell-shaped.

Central Limit Theorem

A fundamental theorem in probability and statistics that states that the distribution of the sum (or average) of a large number of independent, identically distributed random variables approaches a normal distribution.

Sampling

The process of selecting a subset of individuals from a larger population in order to gather information about the population as a whole.

Estimation

The process of using sample data to estimate an unknown population parameter.

Confidence Interval

A range of values within which the true population parameter is likely to fall with a certain level of confidence.

Hypothesis Testing

A statistical method used to make inferences about a population based on sample data.

Null Hypothesis

A statement that assumes there is no significant difference or relationship between variables in a population.

Alternative Hypothesis

A statement that contradicts or negates the null hypothesis and suggests that there is a significant difference or relationship between variables in a population.

Type I Error

Rejecting the null hypothesis when it is actually true.

Type II Error

Failing to reject the null hypothesis when it is actually false.

Regression Analysis

A statistical method used to model the relationship between a dependent variable and one or more independent variables.

Correlation Coefficient

A measure of the strength and direction of the linear relationship between two variables.

Coefficient of Determination

A measure of the proportion of the variance in the dependent variable that can be explained by the independent variables in a regression model.

Outliers

Data points that are significantly different from other observations in a dataset.

Probability and Statistics in Real Life

The application of probability and statistics concepts and techniques in various fields such as finance, healthcare, sports, and social sciences.

Statistical Software Applications

Computer programs and tools used for data analysis, statistical modeling, and visualization.

Data Analysis Techniques

Methods and procedures used to analyze and interpret data in order to extract meaningful insights and make informed decisions.

Descriptive Statistics

Methods used to summarize and describe the main features of a dataset.

Inferential Statistics

Methods used to make inferences and draw conclusions about a population based on sample data.

Probability and Statistics Formulas

Mathematical equations and relationships used to calculate probabilities, perform statistical tests, and estimate parameters.

Mean

The average of a set of numbers, calculated by summing all the values and dividing by the total count.

Median

The middle value in a set of numbers when they are arranged in ascending or descending order.

Mode

The value(s) that occur most frequently in a set of numbers.

Standard Deviation

A measure of the dispersion or variability of a set of numbers, calculated as the square root of the variance.

Variance

A measure of the average squared deviation from the mean, calculated by summing the squared differences between each value and the mean and dividing by the total count.

Covariance

A measure of the relationship between two random variables, indicating the extent to which they vary together.

Probability Density Function

A function that describes the probability distribution of a continuous random variable.

Cumulative Distribution Function

A function that gives the probability that a random variable is less than or equal to a certain value.

Confidence Level

The probability that a confidence interval will contain the true population parameter.

Statistical Significance

A measure of the likelihood that a result or relationship observed in a sample is not due to chance.

Statistical Power

The probability of correctly rejecting the null hypothesis when it is false.

Chi-Square Test

A statistical test used to determine if there is a significant association between two categorical variables.

ANOVA

Analysis of Variance, a statistical test used to compare the means of three or more groups.

Regression Coefficients

The coefficients or weights assigned to the independent variables in a regression model, indicating the strength and direction of their relationship with the dependent variable.

Residuals

The differences between the observed values and the predicted values in a regression model.

Confounding Variable

An extraneous variable that is related to both the independent and dependent variables, leading to a spurious or misleading relationship.

Statistical Hypothesis

A statement about the population parameter(s) that is tested using statistical methods.

Statistical Test

A procedure used to make a decision about a statistical hypothesis based on sample data.

P-value

The probability of obtaining a test statistic as extreme as or more extreme than the observed value, assuming that the null hypothesis is true.

Statistical Inference

The process of drawing conclusions about a population based on sample data, taking into account the uncertainty associated with sampling variability.

Statistical Modeling

The process of formulating and estimating a statistical model to describe the relationship between variables and make predictions or inferences.

Statistical Analysis

The process of organizing, summarizing, interpreting, and presenting data in order to extract meaningful insights and draw valid conclusions.

Statistical Software

Computer programs and tools used for data analysis, statistical modeling, and visualization.

Data Visualization

The graphical representation of data to facilitate understanding, exploration, and communication of patterns, trends, and relationships.

Statistical Error

The difference between the observed value and the true value of a population parameter, due to sampling variability or other sources of uncertainty.

Statistical Bias

A systematic deviation of the estimated value from the true value of a population parameter, due to flaws in the study design or data collection process.