CSE10 3rd Exam

Queuing theory

Is the mathematical study of waiting lines. It analyzes how customers arrive, wait, and are served in a system.

Arrival rate (λ)

Average customers arriving per time

Service rate (μ)

Average customers served per time

Queue discipline

e.g., First Come First Serve (FCFS)

Discrete Probability Distribution

shows probabilities of outcomes for a discrete random variable (countable values).

BINOMIAL DISTRIBUTION

For a binomial random variable X (number of successes in n trials)

MULTINOMIAL DISTRIBUTION

is a generalization of the Binomial Distribution. It describes the probability of outcomes in n independent trials, where each trial can result in more than 2 categories (not just success/failure).

HYPERGEOMETRIC DISTRIBUTION

Used when sampling without replacement from a finite population.

GEOMETRIC DISTRIBUTION

Probability that the first success occurs on the k-th trial.

NEGATIVE BINOMIAL DISTRIBUTION

Probability that the r-th success occurs on the k-th trial

POISSON DISTRIBUTION

Used to model number of events in a fixed interval of time or space

Continuous Probability Distribution

Describes the probability of a continuous random variable that can take any value within an interval.

Normal Distribution

Is a symmetric, bell-shaped distribution defined by: Mean μ, X = observed value

Beta Distribution

A continuous probability distribution defined on the interval: 0 ≤ X ≤ 1

Exponential Distribution

A continuous probability distribution that models the waiting time until the next event occurs, when events happen: Independently or at a constant average rate

Weibull Distribution

Is a continuous probability distribution commonly used to model: Lifetimes of products, Failure times, Reliability of systems

Lognormal Distribution

Is a continuous probability distribution where: ln(X) is normally distributed

Uniform Distribution

Is a continuous probability distribution where all values in a given interval are equally likely. Uniform Because the probability is evenly (uniformly) distributed across the interval.

Normal Distribution

μ (mean), σ (standard deviation)

Beta Distribution

α, β

Gamma Distribution

α, β or k, θ

Exponential Distribution

λ

Chi-square Distribution

χ²

Weibull Distribution

λ (scale), k (shape)