21 сент. 2020 г. · To prove that −1≤Corr(X,Y)≤1, I am using the identity Var( X √ Var(x) − Y √ Var(Y) )≥0. Where does this identity come from? How do I prove it? Proof clarification: For any r.v.s X and Y, −1≤Corr(X,Y)≤1. E(Var(Y|X)) \leq (1 - Math Stack Exchange Другие результаты с сайта math.stackexchange.com

14 дек. 2021 г. · −1≤Corr(X,Y)≤+1. (1) Proof: Consider the variance of X plus or minus Y , each divided by their standard deviations: Var(XσX±YσY).

23 февр. 2016 г. · Population correlation coefficient. The correlation ρ between two variables is: ρ = [ 1 / N ] * Σ { [ (Xi - μX) / σx ] * [ (Yi - μY) / σy…

Theorem: E(XY) = E(X)E(Y), when X is indepen- dent of Y. Proof: For discrete random variables X and Y,. E(XY) = i.

One way to prove that −1≤ρ≤1 is to use the following inequality: αβ≤α2+β ... −1≤ρ(X,Y)≤1;; if ρ(X,Y)=1, then Y=aX+b, where ...

If ρXY = 1, then a > 0, and if ρXY = −1, then a < 0. Proof: Consider the function h(t) defined by h(t) = E((X − µX)t + (Y ...

Let the random variables X and Y have the joint p.m.f.. (a) p(x, y) = 1. 3 ... show that−1 ≤ ρ ≤ 1. Hint consider the discriminant of the non-negative ...

7 дек. 2020 г. · We have to prove that -1 ≤ corr(X,Y) ≤ 1. we know that corr(X,Y) = ρ We have to prove -1 ≤ … View the full answer. answer image blur.

By dividing by the product σXσY of the stan- dard deviations, the correlation becomes bounded between plus and minus 1. −1 ≤ ρXY ≤ 1.