If the correlation coefficient between X and Y is 0.8 and covariance is 121 and the variance of Y is 64, then variance of X will be

Question

Question

Answer 1

Concept:

Some useful formulas are:

The correlation coefficient, r = $\frac{C o v (X, Y)}{σ_{x} \times σ_{y}}$

σ_x = √var X

Calculation:

Given, r = 0.8

Cov (X, Y) = 121

Var Y = 64

r = $\frac{C o v (X, Y)}{σ_{x} \times σ_{y}}$

∴ 0.8 = $\frac{121}{σ_{x} \times \sqrt 64}$ , since Var X = 64, then σ_y = √64 = 8

∴ σ_x = 18.91

∴ √var X = 18.91

∴ var X = 357.59