Jointly Distrubuted Random Variables

Question

Let X and Y be jointly distributed random variables with correlation ρXY ; define the standardized random variables X ~ and Y ~ as X ~ = (X − E(X))/ Var(X) and Y ~ = (Y − E(Y ))/ Var(Y ). Show that Cov(X ~,Y ~) = ρXY .∼

Answer 1

One of the formulas for ρ_xy~ = cov(x~,y~) / [σ_x~σ_y~] but x~ and y~ are standardized so what does that say about σ_x~ and σ_y~ ?

 

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