quanti-prefil

Random Variable

is a function whose domain is a sample space and whose range is some set of real numbers. It is usually denoted by capital or uppercase letters of the English alphabet (e.g., 𝑿), and the possible values of the variables are usually denoted by corresponding lowercase letters (e.g., 𝒙).

Discrete Random Variable

is a random variable that may assume a finite or countable number of possible outcomes that can be listed.

Continuous Random Variable

is a random variable that may assume an uncountable number of values or possible outcomes, represented by the intervals on a number line.

Probability Mass Function (pmf)

provides the probabilities 𝑓(𝑥) = 𝑃(𝑋 = 𝑥) for all possible values that a discrete random variable (𝑥) can take on in the range of 𝑿. This function may be viewed or can be represented as a table, graph, or formula.

Probability Distribution

is a function that describes the shape, character, and relative likelihoods of obtaining the possible values that a random variable can assume.

function

from Set A to Set B is a relation in which each element of the domain is paired with exactly one element of the range. "Each element" implies that every element in the domain is related to some element in the range. "Exactly one" implies that a function is single-valued. It will not give back two (2) or more results for the same input.

domain

of a function is defined as the set of all possible input values (commonly the x variable), which produces a valid output (y-value) from a particular function. In simple language, this is what can go into a function.

range

is the set of all possible output values (commonly the variable y, or sometimes expressed as f(x)), which results from using a particular function. In simple language, this is what actually comes out of a function.

Expected value of a random variable

mean of a probability distribution is the summation of each value of the variable multiplied by its probability. The mean, variance, and standard deviation for samples are calculated differently from the mean, variance, and standard deviation for a probability distribution.

variance

What formula is this random variable with a discrete probability distribution? 2 = ∑(𝑋 − 𝜇𝑥)2 ⋅ 𝑃(𝑋 = 𝑥)

standard deviation

what formula is this in a random variable with a discrete probability distribution? 𝛿 = √𝛅 𝟐

trial.

The experiment is performed for a fixed number of times. Each repetition of the experiment is called

independent.

This means that the outcome of one (1) trial will not affect the outcome of the other trials.

Binomial Distribution

what is this formula? P(r)=r!(n−r)!n!​prqn−r

𝑛 =

the number of trials (sample size)

𝑝 =

the probability of a success on any single trial

𝑟 =

the number of successes in sample, (r = 0, 1, 2, ..., n)

𝑞 =

1 − 𝑝 = the probability of a failure

Poisson Distribution

was developed by French mathematician Simeon Denis Poisson, the Poisson probability distribution is very useful in decision-making with respect to quality control situation, waiting line problems (queue), and other application to business.

Poisson Distribution

P(X=x)=x!μxe−μ what is this formula

𝜇

is the mean number of occurrences per unit (time, volume, area, etc.)

𝑒

is a constant approximately equal to 2.71828... (Actually, 𝑒 is the base of the natural logarithm system.)

𝑥

number of occurrences (0, 1, 2, …)