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Browse all available quizzes, quizbooks, articles, textbooks, SynLearn templates, and SynPrep practice tracks.

1890 learning items

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Showing 673–684 of 1890 items

Quiz

Lognormal, Weibull & Heavy-Tailed Cauchy Distributions

Compare lognormal, Weibull and Cauchy models for positive measurements, reliability lifetimes and heavy-tailed errors. Prerequisites: normal probabilities, logarithms, continuous densities and moments. Work from parameter interpretation to survival calculations, conditional lifetime reasoning and model selection. Explanations distinguish log-scale summaries from original-scale summaries and examine when conventional moments and averaging arguments fail. Cover: Photo by ThisIsEngineering on Pexels. Further reading: [PDF and Common Statistics](https://www.itl.nist.gov/div898/handbook/eda/section3/eda3669.htm), [PDF, CDF, survival and hazard](https://www.itl.nist.gov/div898/handbook/eda/section3/eda3668.htm), [PDF, CDF and Common Statistics](https://www.itl.nist.gov/div898/handbook/eda/section3/eda3663.htm).

statistics

Oct 23, 2026

20 questions

Quiz

Gamma & Beta Distributions

Explore Gamma and Beta distributions through waiting times, random proportions and elementary probability updating. Prerequisites: integration, exponential models, expectation and variance. Practice shape-rate versus shape-scale notation, density normalization, moments, chi-square connections and parameter feasibility. Original calculations and diagnostic challenges explain each alternative and introduce conjugate updating without requiring advanced Bayesian inference. Cover: Photo by ThisIsEngineering on Pexels. Further reading: [4.2.4 Gamma function and Gamma PDF](https://www.probabilitycourse.com/chapter4/4_2_4_Gamma_distribution.php), [Beta PDF and Common Statistics](https://www.itl.nist.gov/div898/handbook/eda/section3/eda366h.htm).

statistics

Oct 23, 2026

25 questions

Quiz

Exponential Distribution & Memoryless Property

Build practical skill in exponential distribution & memoryless property. This 30-question practice set combines single-select and multiselect exercises, worked calculations, explanations of distractors, and diagnostic challenges. Prerequisites: Uniform distributions, conditional probability and exponential functions. Practice includes interpret rate, scale, support and units; compute survival, cdf and interval probabilities; find means, variances and quantiles; use residual-life memorylessness; connect homogeneous poisson arrivals to waits; diagnose mixtures, minima, sums and shifted waits. Questions are independently answerable; the authored learning sequence moves from foundations to applications and assumption checks. Reference methods draw on OpenStax, university probability teaching, and NIST where appropriate.

statistics

Oct 23, 2026

30 questions

Quiz

Continuous Uniform Distribution

Build practical skill in continuous uniform distribution. This 15-question practice set combines single-select and multiselect exercises, worked calculations, explanations of distractors, and diagnostic challenges. Prerequisites: Continuous distributions and CDF transformations. Practice includes interpret uniform density and support; compute interval and conditional probabilities; calculate mean, variance and percentiles; recover endpoints and transform variables; apply the continuous probability integral transform; diagnose arrival assumptions and nonuniform transformations. Questions are independently answerable; the authored learning sequence moves from foundations to applications and assumption checks. Reference methods draw on OpenStax, university probability teaching, and NIST where appropriate.

statistics

Oct 23, 2026

15 questions

Quiz

Linear Combinations of Independent Normal Variables

Build practical skill in linear combinations of independent normal variables. This 25-question practice set combines single-select and multiselect exercises, worked calculations, explanations of distractors, and diagnostic challenges. Prerequisites: Standard normal probabilities and variance rules. Practice includes apply exact normal closure under independence; compute sums and differences of means and variances; analyze weighted combinations and averages; calculate comparison and exceedance probabilities; distinguish shared noise from independent copies; optimize precision and diagnose dependence assumptions. Questions are independently answerable; the authored learning sequence moves from foundations to applications and assumption checks. Reference methods draw on OpenStax, university probability teaching, and NIST where appropriate.

statistics

Oct 23, 2026

25 questions

Quiz

Standard Normal Distribution (Z) & Table Fluency

Build practical skill in standard normal distribution (z) & table fluency. This 35-question practice set combines single-select and multiselect exercises, worked calculations, explanations of distractors, and diagnostic challenges. Prerequisites: Normal PDF properties and elementary algebra. Practice includes standardize measurements and interpret cumulative tables; translate among left, right, central and interval areas; find forward probabilities in original units; invert percentiles to obtain thresholds; recover parameters from quantiles; evaluate conditioning, rounding and alarm design. Questions are independently answerable; the authored learning sequence moves from foundations to applications and assumption checks. Reference methods draw on OpenStax, university probability teaching, and NIST where appropriate.

statistics

Oct 23, 2026

35 questions

Quiz

The Normal Probability Density Function & Properties

Build practical skill in the normal probability density function & properties. This 25-question practice set combines single-select and multiselect exercises, worked calculations, explanations of distractors, and diagnostic challenges. Prerequisites: Continuous expectation, variance and percentiles. Practice includes interpret normal parameters and support; locate mean, median, mode and inflections; analyze shifts and changes in spread; relate density height to units and relative distance; use derivatives and symmetry to analyze shape; diagnose limits of a normal approximation. Questions are independently answerable; the authored learning sequence moves from foundations to applications and assumption checks. Reference methods draw on OpenStax, university probability teaching, and NIST where appropriate.

statistics

Oct 23, 2026

25 questions

Quiz

Expectation, Variance & Percentiles for Continuous RVs

Build practical skill in expectation, variance & percentiles for continuous rvs. This 25-question practice set combines single-select and multiselect exercises, worked calculations, explanations of distractors, and diagnostic challenges. Prerequisites: PDFs, CDFs and integration. Practice includes compute first and second moments by integration; apply lotus to nonlinear costs and transformations; compute variance and squared-error loss; find medians and quantiles; transform quantiles and interpret nonuniqueness; diagnose moment existence and heavy tails. Questions are independently answerable; the authored learning sequence moves from foundations to applications and assumption checks. Reference methods draw on OpenStax, university probability teaching, and NIST where appropriate.

statistics

Oct 23, 2026

25 questions

Quiz

Continuous Random Variables, PDF & CDF Mechanics

Build practical skill in continuous random variables, pdf & cdf mechanics. This 25-question practice set combines single-select and multiselect exercises, worked calculations, explanations of distractors, and diagnostic challenges. Prerequisites: Single-variable integration and probability axioms. Practice includes distinguish density, cumulative probability and point mass; normalize pdfs and integrate interval probabilities; construct and differentiate cdfs; handle conditioning, rounding and support gaps; apply moving-boundary differentiation; diagnose regularity assumptions and invalid densities. Questions are independently answerable; the authored learning sequence moves from foundations to applications and assumption checks. Reference methods draw on OpenStax, university probability teaching, and NIST where appropriate.

statistics

Oct 23, 2026

25 questions

Quiz

Partial Derivatives, Gradients & Multiple Integrals

Build practical skill in partial derivatives, gradients & multiple integrals. This 20-question practice set combines single-select and multiselect exercises, worked calculations, explanations of distractors, and diagnostic challenges. Prerequisites: Single-variable differentiation, integration and optimization. Practice includes compute partial derivatives holding the other coordinate fixed; build gradients and hessians; evaluate iterated integrals; describe and reverse constrained integration regions; use determinants and absolute jacobians; diagnose constrained and unconstrained optima. Questions are independently answerable; the authored learning sequence moves from foundations to applications and assumption checks. Reference methods draw on OpenStax, university probability teaching, and NIST where appropriate.

statistics

Oct 23, 2026

20 questions

Quiz

Optimization & Taylor Approximation

Use derivatives to find extrema and build local approximations. Compare stationary points and boundaries, distinguish local and global maxima, and construct Taylor polynomials, geometric sums and exponential series. Prerequisites: limits, derivatives and basic integration. Challenges address constrained optima, nonattainment on open intervals, curvature-based error direction and explicit remainder bounds. Further reading: Paul Dawkins: Absolute extrema Paul Dawkins: Taylor series Paul Dawkins: Series basics Cover: Photo by Bruno Kraler on Pexels.

statistics

Oct 23, 2026

20 questions

Quiz

Integration, Areas & Improper Integrals

Connect accumulated area with antiderivatives and limits. Practice definite integration, the fundamental theorem, substitution, integration by parts and improper integrals, including elementary probability-area normalization. Prerequisite: limits and derivatives. Analytical questions address signed versus geometric area, singularities, tail convergence and why a curve approaching zero need not have finite area. Further reading: Paul Dawkins: Definite integrals Paul Dawkins: Integration by parts Paul Dawkins: Improper integrals Cover: Photo by Barnabas Davoti on Pexels.

statistics

Oct 23, 2026

20 questions