Discrete vs ContinuousHow the two kinds of random variable differ in every operation.MathematicsDiscreteTakes countably many valuesPMF: P(X = x), summing to 1P(X = x) can be positiveE[X] = Σ x P(X = x)Binomial, Poisson, GeometricThe CDF is a step functionContinuousTakes values across an intervalPDF: f(x) ≥ 0, integrating to 1P(X = x) = 0 for every single xE[X] = ∫ x f(x) dxNormal, Exponential, UniformThe CDF is continuousTHE DIFFERENCE THAT MATTERSFor a continuous variable, only intervals carry probability. A densityis not itself a probability.f(x) may well exceed 1: it is probability per unit x, not probability. Onlyits integral is bounded by 1.Discrete vs Continuouslearnposters.com
Discrete vs Continuous — printable math wall chart from LearnPosters. Free vector PDF, US Letter and A4.

What’s on the Discrete vs Continuous poster

Discrete against Continuous, side by side.

f(x) may well exceed 1: it is probability per unit x, not probability. Only its integral is bounded by 1.

Questions about the Discrete vs Continuous poster

What’s on the Discrete vs Continuous poster?
Discrete against Continuous, side by side. Discrete: Takes countably many values; Discrete: PMF: P(X = x), summing to 1; Discrete: P(X = x) can be positive; Discrete: E[X] = Σ x P(X = x); Discrete: Binomial, Poisson, Geometric; Discrete: The CDF is a step function; Continuous: Takes values across an interval; Continuous: PDF: f(x) ≥ 0, integrating to 1; Continuous: P(X = x) = 0 for every single x; Continuous: E[X] = ∫ x f(x) dx; Continuous: Normal, Exponential, Uniform; Continuous: The CDF is continuous; For a continuous variable, only intervals carry probability. A density is not itself…. f(x) may well exceed 1: it is probability per unit x, not probability. Only its integral is bounded by 1.
Who is the Discrete vs Continuous poster for?
Discrete vs Continuous belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning probability & statistics can pin it up — a beginner, a student mid-course, or someone revising years later.
When should you use the Discrete vs Continuous poster?
Before writing a sum or an integral, settle which kind of variable you have. A wall chart earns its place by being glanceable from where the work is happening, so Discrete vs Continuous belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
What other posters go with Discrete vs Continuous?
Bayes' Theorem, Central Limit Theorem and Conditional Probability sit alongside Discrete vs Continuous in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Bayes' TheoremCentral Limit TheoremConditional Probability
Is the Discrete vs Continuous poster free to download and print?
Yes. Discrete vs Continuous downloads as a free PDF with no account, no email and no watermark, like everything else in the Mathematics section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
What size does the Discrete vs Continuous poster print at?
Discrete vs Continuous is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Discrete vs Continuous loses nothing.Printing guide

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