PROBABILITY AND STATISTICS FOR
ENGINEERING AND THE SCIENCES
COMPREHENSIVE STUDY GUIDE 2026
PROBABILITY THEORY AND STATISTICAL
METHODS
◉ Samples. Answer: Subsets of a population used for analysis.
◉ Populations. Answer: Complete set of items or individuals of
interest.
◉ Probability. Answer: Likelihood of occurrence of an event.
◉ Sampling Procedures. Answer: Methods for selecting samples
from populations.
◉ Measures of Location. Answer: Statistics that describe central
tendency, e.g., mean.
◉ Sample Mean. Answer: Average of values in a sample.
◉ Median. Answer: Middle value when data is ordered.
,◉ Measures of Variability. Answer: Statistics that describe spread of
data, e.g., variance.
◉ Discrete Data. Answer: Data that can take specific values.
◉ Continuous Data. Answer: Data that can take any value within a
range.
◉ Statistical Modeling. Answer: Creating representations of data
relationships.
◉ Graphical Diagnostics. Answer: Visual tools for analyzing data
distributions.
◉ Designed Experiment. Answer: Study where conditions are
controlled by researchers.
◉ Observational Study. Answer: Study where researchers observe
without intervention.
◉ Retrospective Study. Answer: Study analyzing past data to find
correlations.
,◉ Sample Space. Answer: Set of all possible outcomes in a
probability experiment.
◉ Events. Answer: Specific outcomes or sets of outcomes from a
sample space.
◉ Counting Sample Points. Answer: Determining the number of
outcomes in a sample space.
◉ Probability of an Event. Answer: Ratio of favorable outcomes to
total outcomes.
◉ Additive Rules. Answer: Rules for calculating probabilities of
combined events.
◉ Conditional Probability. Answer: Probability of an event given
another event has occurred.
◉ Independence. Answer: Two events are independent if one does
not affect the other.
◉ Product Rule. Answer: Calculates probability of independent
events occurring together.
, ◉ Bayes' Rule. Answer: Calculates conditional probabilities using
prior knowledge.
◉ Random Variable. Answer: Variable whose values depend on
random phenomena.
◉ Discrete Probability Distributions. Answer: Probability
distributions for discrete random variables.
◉ Continuous Probability Distributions. Answer: Probability
distributions for continuous random variables.
◉ Joint Probability Distributions. Answer: Probability distributions
involving two or more random variables.
◉ Mean of a Random Variable. Answer: Expected value calculated
from a probability distribution.
◉ Variance. Answer: Measure of how much values differ from the
mean.
◉ Covariance. Answer: Measure of how two variables change
together.
ENGINEERING AND THE SCIENCES
COMPREHENSIVE STUDY GUIDE 2026
PROBABILITY THEORY AND STATISTICAL
METHODS
◉ Samples. Answer: Subsets of a population used for analysis.
◉ Populations. Answer: Complete set of items or individuals of
interest.
◉ Probability. Answer: Likelihood of occurrence of an event.
◉ Sampling Procedures. Answer: Methods for selecting samples
from populations.
◉ Measures of Location. Answer: Statistics that describe central
tendency, e.g., mean.
◉ Sample Mean. Answer: Average of values in a sample.
◉ Median. Answer: Middle value when data is ordered.
,◉ Measures of Variability. Answer: Statistics that describe spread of
data, e.g., variance.
◉ Discrete Data. Answer: Data that can take specific values.
◉ Continuous Data. Answer: Data that can take any value within a
range.
◉ Statistical Modeling. Answer: Creating representations of data
relationships.
◉ Graphical Diagnostics. Answer: Visual tools for analyzing data
distributions.
◉ Designed Experiment. Answer: Study where conditions are
controlled by researchers.
◉ Observational Study. Answer: Study where researchers observe
without intervention.
◉ Retrospective Study. Answer: Study analyzing past data to find
correlations.
,◉ Sample Space. Answer: Set of all possible outcomes in a
probability experiment.
◉ Events. Answer: Specific outcomes or sets of outcomes from a
sample space.
◉ Counting Sample Points. Answer: Determining the number of
outcomes in a sample space.
◉ Probability of an Event. Answer: Ratio of favorable outcomes to
total outcomes.
◉ Additive Rules. Answer: Rules for calculating probabilities of
combined events.
◉ Conditional Probability. Answer: Probability of an event given
another event has occurred.
◉ Independence. Answer: Two events are independent if one does
not affect the other.
◉ Product Rule. Answer: Calculates probability of independent
events occurring together.
, ◉ Bayes' Rule. Answer: Calculates conditional probabilities using
prior knowledge.
◉ Random Variable. Answer: Variable whose values depend on
random phenomena.
◉ Discrete Probability Distributions. Answer: Probability
distributions for discrete random variables.
◉ Continuous Probability Distributions. Answer: Probability
distributions for continuous random variables.
◉ Joint Probability Distributions. Answer: Probability distributions
involving two or more random variables.
◉ Mean of a Random Variable. Answer: Expected value calculated
from a probability distribution.
◉ Variance. Answer: Measure of how much values differ from the
mean.
◉ Covariance. Answer: Measure of how two variables change
together.
