Is it true that if Corr(X 1 ,X 2 ) 1, then X 1 cX 2 for a c 0 Answer the same question under the additional condition E X 1 E X 2 0 Let m i E X i , i 1,2 Is it true that if Corr(X 1 ,X 2 ) 1, then X 1 m 1 c(X 2 m 2 ) for a c 0 ...

Is it true that if Corr(X 1 ,X 2 ) = 1, then X 1 = cX

Question:

Is it true that if Corr(X₁,X₂) = 1, then X₁ = cX₂ for a c > 0? Answer the same question under the additional condition E{X₁} = E{X₂} = 0. Let m_i = E{X_i}, i = 1,2. Is it true that if Corr(X₁,X₂) = 1, then X₁−m₁ = c(X₂−m₂) for a c > 0?