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Probability

A measure of the likelihood of an event occurring, expressed as a number between 0 and 1.

Classical Probability

Probability based on theoretical arguments, such as rolling a 7 with two dice.

Sample Space

The collection of all possible outcomes of an experiment.

Combination

A selection of items where order doesn't matter.

Independent Events

Events where the occurrence of one doesn't affect the probability of the other.

Permutation

An arrangement of items where order matters.

Conditional Probability

The probability of an event occurring given that another event has already occurred.

Joint Probability

The probability of two events occurring together.

Relative Frequency Definition

Probability based on empirical data, such as past occurrences.

Marginal Probability

The probability of an event occurring irrespective of other events.

Event

A collection of outcomes, such as rolling a 7 or 11 with dice.

Subjective Probability

Probability based on judgment or personal belief.

Experiment

Any process that results in an outcome, like rolling dice.

Key Rules of Probability

Probabilities are between 0 and 1, and the sum of all probabilities is 1.

Outcome

The result observed from an experiment.

Probability of an Event

The sum of probabilities of its outcomes.

Probability of Independent Events

The product of their individual probabilities.

Probability in Business

Helps assess the chances of success for new products or projects.

Probability in Surveys

Used to determine joint and marginal probabilities.

Probability of Respondent Being Female

An example of marginal probability.

Random Variables

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

Bernoulli Distribution

A probability distribution of a random variable which has two possible outcomes, typically 'success' or 'failure'.

Poisson Distribution

A distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space.

Normal Distribution

A continuous probability distribution characterized by a symmetric, bell-shaped curve.

Exponential Distribution

It models the time between events in a Poisson process.

Probability Density Function

A function that describes the likelihood of a random variable to take on a given value.

Cumulative Distribution Function

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

Multiplication Law of Probability

A rule used to find the probability of two independent events occurring together.

Complement

The probability of an event not occurring.

Intersection

The probability of two events both occurring.

Combinations

A selection of items without regard to the order.

Tree Diagram

A visual representation used to map out all possible outcomes of an experiment.

Discrete Random Variables

Random variables that have countable outcomes.

Continuous Random Variables

Random variables that have an infinite number of possible values.

Probability Playground

A conceptual space to explore and understand different probability concepts through games of chance.

Detective and Probability

Uses conditional probability, to see how one event affects another.

Probability Toolbox

Essential instruments like combinations and permutations for solving probability problems.

Tree Diagram Use

Mapping out all possible outcomes of an experiment.

Significance of Normal Distribution

It represents many natural phenomena with a symmetric, bell-shaped curve.

Poisson Distribution Purpose

The number of times an event can occur over a span of time

Exponential Distribution Purpose

The time between events, like waiting for your turn at a game.

Role of Combinations in Probability

To choose groups without worrying about order.

Role of Permutations in Probability

To focus on the sequence of arrangement.

Random Variables

Variables that can take on different values, representing outcomes of a random phenomenon.

Discrete

A type of random variable with countable outcomes.

Continuous

A type of random variable with an infinite number of possible values.

Binomial Distribution

A distribution showing the number of successes in a series of independent trials.

Probability Density Function

A function that describes the likelihood of a continuous random variable taking on a specific value.

Cumulative Distribution Function

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

Conditional Probability

The probability of an event occurring given that another event has already occurred.

Multiplication Law of Probability

A rule for finding the probability of two independent events occurring together.

Business Analytics

A tool for making informed decisions by analyzing past data and trends.

Descriptive Analytics

Helps you understand what happened by examining past data.

Predictive Analytics

Uses patterns from the past to forecast future events.

Prescriptive Analytics

Suggests actions to achieve desired outcomes.

Interval

Order matters and no true zero starting point

Grocery Shopping

How can business analytics help in everyday tasks like managing your grocery list?

ordinal

Ranking/ placement order matter

Analysis of Variance (ANOVA) calculates the p-value corresponding to the test statistic using which of the following distributions?

F-distribution

Historical Data

What does predictive analytics use to forecast future events?

ratio data

has zero starting point and order matters

The larger the p-value

the more evidence against the null hypothesis

IF Function

A logical function in Excel used to make decisions based on certain conditions.

INDEX Function

A lookup function in Excel that finds data based on row and column numbers.

As the sample size increases, the

standard error of the mean decreases

VLOOKUP Function

A lookup function in Excel that retrieves data based on a reference value.

Logical Functions

Functions in Excel that help make decisions based on data conditions.

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

becomes smaller

Data Queries

Processes like sorting and filtering that help manage and analyze data.

Clustered Column Chart

A chart type used to compare different groups or categories side by side.

Stacked Column Chart

A chart type that highlights the total change by stacking data segments.

Pie Charts Use

They show proportions.

Scatter Diagram

A chart type that reveals relationships between variables.

#VALUE!

error in function

Unimodal Distribution

A distribution with one clear peak.

Categorical (Nominal) Data

Data sorted into categories without any inherent order.

Kurtosis

A measure of the 'tailedness' of a distribution.

High Kurtosis Indication

Indicates more data points are in the tails.

Skewness

A measure of the asymmetry of a distribution.

Positive Skewness Meaning

The tail is on the right, with more data points on the left.

Low Kurtosis Indication

Indicates a more uniform distribution.

Negative Skewness Meaning

The tail is on the left, with more data points on the right.

Continuous Distributions

Uniform, Normal, Exponential, and Triangular

Random Sampling

A sampling method where every individual has an equal chance of being selected.

Stratified Sampling

Divides the population into subgroups and samples from each.

Cluster Sampling

Focuses on groups to save time but risks homogeneity.

Point Estimates

Best guesses of population parameters.

Standard Error Measurement

Measures variation from the true population parameter.

Empirical Rules

Guidelines used to analyze sampling errors.

Sampling Distributions

Show how sample statistics vary, crucial for statistical inference.

Standard Error of the Mean

Indicates variation of sample means from the true population mean.

Confidence Interval

A range for the true population parameter with a certain level of confidence.

Difference Between Confidence and Prediction Intervals

Confidence focuses on population parameters, prediction on individual data points.

Sample Size Importance

Crucial for constructing accurate confidence intervals.

Sample Size Effect on Confidence Intervals

Larger samples reduce the margin of error.

Standard Error and Sample Size Relationship

Larger samples reduce the standard error.

Empirical Rules Purpose

Ensure estimates are informed.

Null Hypothesis

The assumption that there is no effect or change.

Alternative Hypothesis

The hypothesis suggesting there is a change or effect.

Analysis of Variance (ANOVA)

A statistical method to determine significant differences between group means.