PROBABILITY AND STATISTICS FOR
ENGINEERING AND THE SCIENCES EXAM
PREPARATION PACK 2026 KEY CONCEPTS
AND REVISION NOTES
◉ Chebyshev's Theorem. Answer: Estimates the proportion of
values within k standard deviations.
◉ Binomial Distribution. Answer: Probability distribution of binary
outcomes over trials.
◉ Multinomial Distribution. Answer: Generalization of binomial
distribution for more than two outcomes.
◉ Hypergeometric Distribution. Answer: Probability distribution for
sampling without replacement.
◉ Negative Binomial Distribution. Answer: Models number of
failures before success.
◉ Geometric Distribution. Answer: Models number of trials until
first success.
,◉ Poisson Distribution. Answer: Models number of events in fixed
interval.
◉ Poisson Process. Answer: Describes events occurring randomly
over time.
◉ Continuous Uniform Distribution. Answer: All outcomes equally
likely over an interval.
◉ Normal Distribution. Answer: Symmetrical distribution defined
by mean and variance.
◉ Areas under the Normal Curve. Answer: Represents probabilities
for normal distribution.
◉ Applications of Normal Distribution. Answer: Used in statistics for
real-world data modeling.
◉ Normal Approximation to the Binomial. Answer: Approximates
binomial distribution using normal distribution.
◉ Gamma Distribution. Answer: Models waiting times for Poisson
processes.
,◉ Exponential Distribution. Answer: Models time between events in
Poisson process.
◉ Chi-Squared Distribution. Answer: Used in hypothesis testing and
confidence intervals.
◉ Beta Distribution. Answer: Models random variables limited to
interval [0, 1].
◉ Lognormal Distribution. Answer: Models variables whose
logarithm is normally distributed.
◉ Weibull Distribution. Answer: Models life data and reliability
analysis.
◉ Random Sampling. Answer: Each member has equal chance of
selection.
◉ Sampling Distributions. Answer: Distribution of sample statistics
over many samples.
◉ Central Limit Theorem. Answer: Sample means approach normal
distribution as sample size increases.
, ◉ t-Distribution. Answer: Used for small sample sizes in hypothesis
testing.
◉ F-Distribution. Answer: Used to compare variances between two
populations.
◉ Statistical Hypotheses. Answer: Statements about population
parameters to be tested.
◉ P-Values. Answer: Probability of observing data given null
hypothesis.
◉ Maximum Likelihood Estimation. Answer: Estimates parameters
maximizing likelihood of observed data.
◉ Prediction Intervals. Answer: Range within which future
observations are expected.
◉ Tolerance Limits. Answer: Range within which a specified
proportion of data falls.
◉ Single Sample Estimation. Answer: Estimates population
parameters from one sample.
ENGINEERING AND THE SCIENCES EXAM
PREPARATION PACK 2026 KEY CONCEPTS
AND REVISION NOTES
◉ Chebyshev's Theorem. Answer: Estimates the proportion of
values within k standard deviations.
◉ Binomial Distribution. Answer: Probability distribution of binary
outcomes over trials.
◉ Multinomial Distribution. Answer: Generalization of binomial
distribution for more than two outcomes.
◉ Hypergeometric Distribution. Answer: Probability distribution for
sampling without replacement.
◉ Negative Binomial Distribution. Answer: Models number of
failures before success.
◉ Geometric Distribution. Answer: Models number of trials until
first success.
,◉ Poisson Distribution. Answer: Models number of events in fixed
interval.
◉ Poisson Process. Answer: Describes events occurring randomly
over time.
◉ Continuous Uniform Distribution. Answer: All outcomes equally
likely over an interval.
◉ Normal Distribution. Answer: Symmetrical distribution defined
by mean and variance.
◉ Areas under the Normal Curve. Answer: Represents probabilities
for normal distribution.
◉ Applications of Normal Distribution. Answer: Used in statistics for
real-world data modeling.
◉ Normal Approximation to the Binomial. Answer: Approximates
binomial distribution using normal distribution.
◉ Gamma Distribution. Answer: Models waiting times for Poisson
processes.
,◉ Exponential Distribution. Answer: Models time between events in
Poisson process.
◉ Chi-Squared Distribution. Answer: Used in hypothesis testing and
confidence intervals.
◉ Beta Distribution. Answer: Models random variables limited to
interval [0, 1].
◉ Lognormal Distribution. Answer: Models variables whose
logarithm is normally distributed.
◉ Weibull Distribution. Answer: Models life data and reliability
analysis.
◉ Random Sampling. Answer: Each member has equal chance of
selection.
◉ Sampling Distributions. Answer: Distribution of sample statistics
over many samples.
◉ Central Limit Theorem. Answer: Sample means approach normal
distribution as sample size increases.
, ◉ t-Distribution. Answer: Used for small sample sizes in hypothesis
testing.
◉ F-Distribution. Answer: Used to compare variances between two
populations.
◉ Statistical Hypotheses. Answer: Statements about population
parameters to be tested.
◉ P-Values. Answer: Probability of observing data given null
hypothesis.
◉ Maximum Likelihood Estimation. Answer: Estimates parameters
maximizing likelihood of observed data.
◉ Prediction Intervals. Answer: Range within which future
observations are expected.
◉ Tolerance Limits. Answer: Range within which a specified
proportion of data falls.
◉ Single Sample Estimation. Answer: Estimates population
parameters from one sample.
