What’s on the Expectation & Variance poster
A 7-row table: Expression · Equals.
a and b are constants; X and Y are random variables.
- E[aX + b] — a E[X] + b
- E[X + Y] — E[X] + E[Y], always
- E[XY], X and Y independent — E[X] E[Y]
- Var(X) — E[X²] − (E[X])²
- Var(aX + b) — a² Var(X)
- Var(X + Y), independent — Var(X) + Var(Y)
- Var(X + Y), in general — Var X + Var Y + 2Cov(X, Y)
Expectation is linear with no independence assumption at all. Variance is not, and that is precisely where independence is needed.
Questions about the Expectation & Variance poster
- What’s on the Expectation & Variance poster?
- A 7-row table: Expression · Equals. a and b are constants; X and Y are random variables. E[aX + b] — a E[X] + b; E[X + Y] — E[X] + E[Y], always; E[XY], X and Y independent — E[X] E[Y]; Var(X) — E[X²] − (E[X])²; Var(aX + b) — a² Var(X); Var(X + Y), independent — Var(X) + Var(Y); Var(X + Y), in general — Var X + Var Y + 2Cov(X, Y). Expectation is linear with no independence assumption at all. Variance is not, and that is precisely where independence is needed.
- Who is the Expectation & Variance poster for?
- Expectation & Variance 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 Expectation & Variance poster?
- For combining random variables without recomputing a distribution from scratch. A wall chart earns its place by being glanceable from where the work is happening, so Expectation & Variance belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
- What other posters go with Expectation & Variance?
- Bayes' Theorem, Central Limit Theorem and Conditional Probability sit alongside Expectation & Variance 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 Expectation & Variance poster free to download and print?
- Yes. Expectation & Variance 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 Expectation & Variance poster print at?
- Expectation & Variance 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 Expectation & Variance loses nothing.Printing guide
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