Foundations of Computing - Poisson Distribution

These flashcards cover key concepts related to Poisson distributions, their approximations using normal distributions, and relevant statistical terms discussed in the lecture.

Poisson Distribution

A statistical model for events that are randomly distributed in time/space, characterized by a mean number of events in a fixed period.

Random Variable (X)

A variable representing a numerical outcome of a random phenomenon; X ∼ Po(λ) indicates it follows a Poisson distribution with mean λ.

Cumulative Poisson Probability

The probability that a Poisson random variable takes a value less than or equal to a specific value x; denoted as P(X ≤ x).

Normal Distribution

A continuous probability distribution characterized by a bell-shaped curve, defined by mean μ and standard deviation σ; denoted as X ∼ N(μ, σ²).

Continuity Correction

An adjustment made when using a normal distribution to approximate a discrete distribution; it involves using x ± 0.5.

Standard Normal Variable (Z)

A normal variable with a mean of 0 and a standard deviation of 1, typically used for standardization of normal distributions.

λ (Lambda)

The mean number of events in a Poisson distribution; it also serves as the mean and standard deviation when approximating with a normal distribution.

Probability Density Function

A function that describes the likelihood of a continuous random variable to take a specific value; areas under the curve represent probabilities.

P(X=x)

The probability of a precise count of events (x) occurring in a Poisson distribution, computable through the formula P(X=x) = (e^(-λ) * λ^x) / x!.

P(Y < x + 0.5)

The probability of a continuous random variable Y being less than x + 0.5, used in conjunction with continuity correction for approximating probabilities.