Expectation and Variance

Statistics — Third Secondary

Common mistakes

Comparison aspect	Main idea	Keywords
Using μ² in place of Σ x² f(x)	the shortcut formula needs the sum of column 4 first and then μ² is subtracted	shortcutformulaneedscolumn
Forgetting to square the expectation	μ² means the square of the expectation not the expectation itself	meansitself
Adding the constant to the variance	Var(X + b) = Var(X) while Var(aX) = a² Var(X)	while
Treating the expectation as a value that actually occurs	the expectation is a long-run average and may not be a possible value of the variable	longaveragepossiblevariable
Confusing the actual gain with the expected gain	a player may win in one game but the expectation shows the general trend over the long run	playergameexpectationshows

Expectation and Variance · 6 / 7