Chapter 5 Business Analytics

What information is included in a contingency table?

A contingency table includes the number of individuals in each event, the probability of each event, and the joint probability of the two events.

What is a contingency table?

A contingency table is a tabular representation of the joint probability of two events.

How is a contingency table used?

A contingency table is used to compare two or more events, such as the probability of two different products being purchased.

What is a discrete probability distribution?

A discrete probability distribution is a probability distribution with a discrete set of outcomes, such as the sum of two dice.

What is a joint probability in a contingency table?

A joint probability in a contingency table is the probability of two events occurring together.

How is a joint probability derived?

A joint probability is derived as P(A ∩ B)=P(A)*P(B|A).

What is a marginal probability in a contingency table?

A marginal probability in a contingency table is the probability of an event occurring, regardless of any other events.

What is a probability distribution?

A probability distribution is a table or graph that shows all of the possible outcomes of a random variable and the probability of each outcome occurring.

What is a random variable?

A random variable is a numerical representation of the outcomes of an experiment or process. It can be discrete (e.g. the sum of two dice) or continuous (e.g. the return of a mutual fund).

What is an event in probability?

An event in probability is one or more outcomes. An event is a subset of the sample space.

What is an event?

An event is an occurrence that has a certain probability of occurring.

What is an experiment?

An experiment is a process or action that is performed in order to observe an outcome.

What is an outcome?

An outcome is the result of an experiment or process.

What is the Bayes' theorem?

Bayes' theorem is a formula used to calculate the conditional probability of an event A given the occurrence of another event B.

What is classical probability?

Classical probability assumes that all outcomes of an experiment are equally likely.

What is the purpose of classical probability?

Classical probability is used to assign equal chance to each outcome of an experiment, such as flipping a coin.

What is conditional probability?

Conditional probability is the probability of an event occurring given that some other condition is satisfied.

What are continuous random variables?

Continuous random variables are random variables that can assume any value within some interval.

What is correlation?

Correlation is a measure of how closely two variables are related to each other.

What is the difference between descriptive and inferential statistics?

Descriptive statistics are used to describe data, while inferential statistics are used to make inferences about a population from a sample.

How do we calculate descriptive statistics from data?

Descriptive statistics from data can be calculated by computing the mean and standard deviation.

What are discrete random variables?

Discrete random variables are random variables that can only assume a countable number of outcomes.

How can empirical probability be used?

Empirical probability can be used most in business analytics to make decisions based on data.

What is an example of the addition rule?

For example, if the probability of event A is 0.3 and the probability of event B is 0.6, the probability of event A or B occurring is 0.3 + 0.6 - 0.18 = 0.78.

What is an example of the complement rule?

For example, if the probability of event A is 0.5, the probability of the complement of event A is 1-0.5 = 0.5.

What is the difference between independent and dependent events?

Independent events are events that are not affected by the occurrence or non-occurrence of other events, while dependent events are events that are affected by the occurrence or non-occurrence of other events.

What is linear regression?

Linear regression is a statistical technique used to estimate the relationship between two variables, where one is the dependent variable and the other is the independent variable.

What are mutually exclusive events?

Mutually exclusive events are events that cannot occur at the same time.

What is the difference between population and sample statistics?

Population statistics refer to the characteristics of a population, while sample statistics refer to the characteristics of a sample drawn from a population.

What is probability?

Probability is a measure of the likelihood of an event occurring.

What is an example of an experiment that involves uncertainty?

Rolling two dice is an example of an experiment that involves uncertainty.

What is the difference between subjective probability and empirical probability?

Subjective probability is based on personal judgement or experience, whereas empirical probability is based on observed relative frequency.

What is subjective probability?

Subjective probability is based on personal judgement or experience.

What is the Poisson probability distribution?

The Poisson probability distribution is a discrete probability distribution used to describe the probability of a certain event occurring k times in a fixed interval of time or space.

What is the purpose of the addition rule?

The addition rule is used to calculate the probability that event A or B occurs, P(A U B) = P(A) + P(B) - P(A ∩ B).

What is the addition rule?

The addition rule states that the probability that event A or B occurs is, P(A U B) = P(A) + P(B) - P(A ∩ B).

What is the binomial distribution?

The binomial distribution is a probability distribution used to describe the probability of a certain event occurring k times in n trials.

What is the complement of an event?

The complement of an event is the event consisting of all outcomes that are not in the original event. The complement of an event is denoted by A c ,

What is the relationship between the complement rule and the addition rule?

The complement rule and the addition rule are related in that they both deal with probabilities of events, but the complement rule deals with the probability of the complement of an event while the addition rule deals with the probability of two events occurring together.

What is the covariance of two variables?

The covariance of two variables is a measure of the degree to which the variables vary together, that is, the degree to which one variable increases when the other increases.

What is the expected value of a random variable?

The expected value of a random variable is a weighted average of the possible values of the random variable, where each outcome is weighted by its probability of occurring.

What is the expected value of an experiment?

The expected value of an experiment is the average outcome when the experiment is repeated many times.

What is the event consisting of all outcomes that are in both A and B?

The intersection of the two events A and B, denoted by A ∩ B,

What is the intersection of two events?

The intersection of two events is the event consisting of all outcomes that are in both A and B. The intersection of two events is denoted by A ∩ B,

What is the joint probability of two events?

The joint probability of two events is the probability of both events occurring together, and is also referred to as P(A∩B).

What is the language of probability?

The language of probability is the language used to describe events and their probabilities.

What is the law of total probability?

The law of total probability states that the probability of an event is equal to the sum of the probabilities of the mutually exclusive and exhaustive events that make up the event.

What is the mean and standard deviation used to measure?

The mean and standard deviation are used to measure uncertainty.

What is the normal distribution?

The normal distribution is a continuous probability distribution used to describe the probability of a certain event occurring in a given interval of values.

What is the outcome when rolling two dice?

The outcome when rolling two dice is one of the 36 possible rolls.

What is the outcome when rolling two six-sided die?

The outcome when rolling two six-sided die is one of the 36 possible rolls.

What are some possible outcomes when rolling two dice?

The possible outcomes when rolling two dice include rolling a number less than 4, rolling a number greater than 10, and rolling a 4, 5, 6, 7, 8, 9 or 10.

What is the probability distribution of a random variable?

The probability distribution of a random variable is a graph or table that shows the probabilities of all possible values of the random variable.

How is the probability of A given B derived?

The probability of A given B is derived as P(A|B)=P(A ∩ B)/P(B).

What is the probability of an event occurring?

The probability of an event occurring is a number between zero and one. If the probability is zero, the event is impossible; if the probability is one, the event will occur with certainty.

What is the probability of rolling a 3 on a white die and a 5 on a red die?

The probability of rolling a 3 on a white die and a 5 on a red die is 1/36.

What is the probability of rolling a 5 on a red die?

The probability of rolling a 5 on a red die is 1/6.

What is the probability of two events occurring in succession?

The probability of two events occurring in succession is equal to the product of the probabilities of the individual events.

What is the sample space of an experiment?

The sample space of an experiment is the set of all possible outcomes.

What is the standard deviation of a random variable?

The standard deviation of a random variable is a measure of the spread of its probability distribution.

What is the sum of the probabilities of mutually exclusive and exhaustive events?

The sum of the probabilities of mutually exclusive and exhaustive events equals 1.

What are the three important definitions related to probability?

The three important definitions related to probability are union, intersection, and complement.

What are the two key properties of a discrete probability distribution?

The two key properties of a discrete probability distribution are that each probability must be between 0 and 1, and that the sum of all of the probabilities must equal 1.

What are the two types of probability distributions?

The two types of probability distributions are discrete and continuous.

What is the notation for the union, intersection, and complement?

The union of two events is denoted by A U B,

What is the union of two events?

The union of two events is the event consisting of all outcomes in either event. The union of two events is denoted by A U B,

What does it mean for two events to be dependent?

Two events are dependent if the occurrence of one event affects the probability of the occurrence of the other.

What does it mean for two events to be independent?

Two events are independent if the occurrence of one event does not affect the probability of the occurrence of the other.