DADM Chapter 5: Probability and Random Variables

Comprehensive vocabulary flashcards covering probability concepts, probability distributions, discrete versus continuous random variables, and subjective versus objective probabilities.

Probability Tree

A graphical representation of an uncertain situation used to calculate conditional and joint probabilities across sequential events.

Addition Rule for Mutually Exclusive Events

A rule stating that the probability of an event is the sum of the probabilities of disjoint paths leading to it, exemplified by $P(A) = P(A \text{ and } B) + P(A \text{ and } \bar{B}) = \frac{1}{2} + \frac{1}{15} = \frac{17}{30} \text{ or } 0.5667$.

Objective Probabilities

Probabilities that can be estimated from long-run proportions.

Relative Frequency

The proportion of times an event occurs out of the total number of times the random experiment is run.

Law of Large Numbers

A mathematical result stating that the relative frequency of an event, in the long run, will get closer and closer to the "true" probability of the event.

Subjective Probability

One person's assessment of the likelihood that a certain event will occur, typically used when situations cannot be repeated under identical conditions.

Discrete Random Variable

A random variable that has only a finite number of possible values, typically resulting from a count.

Continuous Random Variable

A random variable that has a continuum of possible values, usually resulting from a measurement and requiring calculus for a proper mathematical treatment.

Discrete Probability Distribution

A specification of the possible values of a random variable $X$ (denoted $x_1, x_2, \text{...}, x_k$) alongside their corresponding probabilities, denoted as $P(X = x_i)$ or $p(x_i)$.

Criteria for Probability Distributions

The two mandatory mathematical properties of any discrete probability distribution: all probabilities must be nonnegative, and the probabilities must sum to $1$.

Cumulative Probability

The probability that a random variable is less than or equal to a particular value, denoted as P(X \timesle x) and calculated by summing the probabilities of all values less than or equal to that value.