COHP 350 Quiz 3 Review: Probability Distributions

Vocabulary flashcards covering discrete and continuous probability distributions, including uniform, exponential, and hypergeometric models, formula applications, and graphical properties from COHP 350 Quiz 3.

Continuous Probability as Area

The principle that for a continuous random variable, the area under the probability density curve between two points represents the probability of that interval, expressed in notation such as $P(2 \le x \le 6)$ or $P(1.75 < x < 4.35)$.

Continuous Uniform Distribution Mean ($\mu$)

The long-term, expected average waiting time for a uniform distribution spanning interval $[a, b]$, calculated using the formula $\mu = \frac{a + b}{2}$.

Continuous Uniform Distribution Standard Deviation ($\sigma$)

The measure of dispersion for a uniformly distributed continuous random variable over $[a, b]$, calculated using the formula $\sigma = \sqrt{\frac{(b - a)^2}{12}}$.

Probability Density Function (pdf)

A graphical representation that uses the notation $f(x)$ to represent the curved or flat boundary line of a continuous probability distribution.

Cumulative Distribution Function (cdf)

A function that describes the accumulated area under the probability density curve as a cumulative probability up to a specified value.

Exponential (Decay) Distribution

A continuous probability distribution characterized by having more small values, fewer large values, an optional decay parameter, and common application in evaluating product reliability.

Distribution Selection Principle

The rule stating that data types and how they are used determine the choice between discrete and continuous random variable distributions, which subsequently guides appropriate statistical formulas and accurate probability calculations.

Discrete Random Variable Probability Distributions

A family of distributions modeling countable outcomes—including geometric, binomial, hypergeometric, and Poisson distributions—which explicitly excludes continuous models such as the exponential distribution.

Uniform Distribution (Graphical Shape)

A probability distribution depicted graphically by a rectangular density function where $f(x)$ maintains a constant horizontal level between boundary parameters $a$ and $b$.

Expected Value ($\mu$)

The long-term average or sum of a discrete probability distribution, calculated by summing the products of each value and its respective probability: $\mu = \sum x \cdot P(x)$.

Hypergeometric Distribution

A discrete probability distribution used when sampling without replacement from two distinct groups, such as selecting a clinical trial cohort of $n = 10$ from $15$ males and $23$ females to determine $P(x = 7)$.

Time-to-Failure Modeling

A reliability analysis scenario—such as Flexall calculating the probability that artificial hip joints remain functional between $8.5$ and $12.75$ years—best modeled using an exponential distribution.