zuai-logo

Glossary

B

Binomial Distribution

Criticality: 3

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

Example:

Counting how many times you correctly guess on 10 multiple-choice questions would involve a binomial distribution.

D

Discrete

Criticality: 2

A characteristic of a random variable indicating it can only take on a countable number of distinct values, typically whole numbers.

Example:

The number of flips it takes to get the first head is a discrete variable, as you can't have 2.5 flips.

F

First Success Focus

Criticality: 3

The defining characteristic of a geometric distribution, where the variable of interest is the trial number on which the very first success occurs.

Example:

If you're waiting for the first time a specific song plays on the radio, you have a first success focus.

G

Geometric Random Variable

Criticality: 3

A discrete random variable that counts the number of independent trials needed to obtain the first success.

Example:

The number of times a basketball player shoots until they make their first basket is a geometric random variable.

I

Independent Trials

Criticality: 2

A condition where the outcome of one trial does not influence the outcome of any subsequent trials.

Example:

When drawing cards with replacement, each draw is an independent trial because the deck's composition resets.

M

Mean (Expected Value)

Criticality: 3

The average number of trials one would expect to need to achieve the first success in a geometric distribution, calculated as 1/p.

Example:

If the probability of hitting a target is 0.2, the mean (expected value) number of shots until the first hit is 1/0.2 = 5 shots.

P

Probability Mass Function (PMF)

Criticality: 2

A function that gives the probability that a discrete random variable is exactly equal to some specific value.

Example:

Using the Probability Mass Function, you can calculate the exact chance that the first person to correctly answer a trivia question is the 7th person asked.

S

Skewed Right

Criticality: 2

A characteristic shape of a distribution where the tail extends further to the right, indicating that most of the data points are concentrated on the lower end.

Example:

A histogram showing the number of attempts until a first success will typically be skewed right, as it's more likely to succeed early.

Standard Deviation

Criticality: 2

A measure of the typical variability or spread of the number of trials around the mean in a geometric distribution.

Example:

A high standard deviation for the number of attempts to get a first success means the actual number of attempts can vary greatly from the average.

T

Two Outcomes

Criticality: 2

A condition for Bernoulli trials where each trial can only result in one of two possibilities: success or failure.

Example:

Deciding if a customer makes a purchase or not represents the two outcomes needed for a geometric setting.

g

geometricCDF

Criticality: 2

A calculator function used to find the cumulative probability that the first success in a geometric distribution occurs on or before a specific trial 'k'.

Example:

If you want to know the probability that you find a parking spot within 3 attempts, you'd use geometricCDF.

geometricPDF

Criticality: 2

A calculator function used to find the probability that the first success in a geometric distribution occurs on a specific trial 'k'.

Example:

To find the probability that the first time you roll a 'snake eyes' (double ones) is on your 5th roll, you would use geometricPDF.