In the Journal of Hydrological Sciences (April 2000), the bivariate normal distribution was used to model the joint distribution of annual storm peak (i.e., maximum rainfall intensity) and total yearly rainfall amount in Tokushima, Japan. Let X represent storm peak and Y represent total amount of rainfall. Then the bivariate normal distribution is given by

where μ_x and μ_y are the means for X and Y, respectively, and σ_x and σ_y are the standard deviations for X and Y, respectively. Use the properties of density functions to show that when ρ = 0, X and Y are independent.

Transcribed Image Text:

1 f(x, y) ச,ச,Vi - 1 exp 2(1 - p?) Y HY X - X. Y- Hy - 2p