Refer to the Journal of Hydrological Sciences (April 2000) study of rainfall in Tokushima, Japan, Exercise 6.34. Recall that the bivariate normal distribution was used to model the joint distribution of annual storm peak X (millimeters/day) and annual rainfall amount Y (millimeters). The article used the following values as estimates of the distribution’s parameters: μ_x = 147 mm/day, σ_x =  mm/day, μ_y  = 223 mm, and σ_y = 117 mm, and ρ = .67. Use this information to find the covariance between X and Y.

Data from Exercise 6.34

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

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1 f(x, y): 2moz0,V1 - p 1 exp 2(1 - p?) Y My Y - 2p