A rock specimen from a particular area is randomly selected and weighed two different ti...

A rock specimen from a particular area is randomly selected and weighed two different times. Let W denote the actual weight and X₁ and X₂ the two measured weights. Then X₁ = W + E₁ and X₂ = W + E₂, where E₁ and E₂ are the two measurement errors. Suppose that the E_is are independent of one another and of W and that .

a. Express r, the correlation coefficient between the two measured weights X₁ and X₂, in terms of σ²_W , the variance of actual weight, and σ²_x, the variance of measured weight.

b. Compute ρ when σ_W _ 1 kg and σ_E _ .01 kg.