Quantitative Techniques COQT111 Unit 3 Quiz

A probability value always lies between 0 and 1, inclusive (i.e. 0 ≤ 𝑃(𝐴) ≤ 1).

If it is impossible for an event to occur, then 𝑃(𝐴) = 0.

If it is certain that an event will occur, then 𝑃(𝐴) = 1.

The sum of the probabilities of all possible events in a sample space equals 1 (i.e. for 𝑘 possible events in a sample space, 𝑃(𝐴1 ) + 𝑃(𝐴2 ) + 𝑃(𝐴3 ) + ⋯ + 𝑃(𝐴𝑘 ) = 1).

If 𝑃(𝐴) is the probability of event A occurring, then the probability of event A not occurring (i.e. Ā) is defined as 𝑃(𝐴) = 1 − 𝑃(𝐴).

The intersection of events refers to the occurrence of both events simultaneously.

The union of events refers to the occurrence of at least one of the events.

Mutually exclusive events cannot occur simultaneously.

The probability of a single event occurring. It's calculated using values on the margins of a frequency table.

The probability of two or more events happening simultaneously. It's calculated using the value at the intersection of the corresponding rows and columns in a cross-tabulation.

The probability of event A happening given that event B has already occurred. It's like event B setting the stage for event A.

The probability of either event A or event B occurring in a single trial of a random experiment, specifically when events A and B can happen together.

The probability of event A occurring given that event B has already happened. This is like event B setting the stage for event A.

In a single trial of a random experiment, the probability of both event A and event B happening together. This applies when the events are dependent.

The probability of either event A or B happening in a single trial when they have no overlapping outcomes.

The formula used to find the joint probability of two dependent events occurring together in a single trial of a random experiment.

The probability of event A not happening when event B is certain to happen. It's like the probability of A when B has already occurred.

The product of consecutive positive integers from 𝑛 down to 1, denoted as 𝑛!

A way to count the number of ways to arrange a subset of objects from a larger set, where the order of selection matters.

The number of different ways to arrange 𝑟 objects from 𝑛 objects when order matters, calculated as 𝑛! / (𝑛 − 𝑟)!

A way to count the number of ways to select a subset of objects from a larger set, where the order of selection doesn't matter.

The number of ways to select 𝑟 objects from 𝑛 objects when order doesn't matter, calculated as 𝑛! / (𝑟! * (𝑛 − 𝑟)!)

The total number of outcomes for multiple events is found by multiplying the number of outcomes for each individual event.

If an event has 𝑛1 possible outcomes, 𝑛2 possible outcomes, etc., the total number of outcomes is 𝑛1 × 𝑛2 × ... × 𝑛𝑗.

The number of possible arrangements of objects where order is significant. It's a specific type of permutation where all objects are arranged.

A mathematical formula used to calculate the number of ways to choose r objects from a set of n objects, without regard to order.

A function that assigns probabilities to each possible outcome of a random variable, illustrating the likelihood of different values.

A probability distribution where the random variable can only take on discrete (often whole number) values.

A probability distribution where the random variable can take on any value within a continuous range.

A type of discrete probability distribution that describes the probability of a certain number of successes in a fixed number of trials.

A type of discrete probability distribution that describes the probability of a certain number of events occurring in a fixed interval of time or space.

A type of continuous probability distribution that is bell-shaped and symmetrical.

A process where events occur independently and at a constant rate within a given time, space, or volume interval.

The probability of a fixed number of events occurring in a specified interval, where the average rate of events is known.

The average number of events that occur in a given time, space, or volume interval.

The formula used to calculate the probability of observing a specific number of events (x) in a Poisson process, given the average rate (λ).

The range of possible values for the number of events (x) in a Poisson process, from zero to infinity.

The constant 'e' in the Poisson probability formula, approximately equal to 2.71828.

The probability of observing zero events in a given interval.

Examples of real-world phenomena that can be modeled using a Poisson process.