... thedistribution. (See Fig. 3. 12. )Clearly, f(x1, x 2 ) > 0. That ∫∫ޒ 2 f(x1, x 2 )dx1dx 2 = 1 is seen as follows: 12 1 2 111 2 111 22 2 22 2 2 22 2111 2 2−()=−⎛⎝⎜⎞⎠⎟−−⎛⎝⎜⎞⎠⎟−⎛⎝⎜⎞⎠⎟+−⎛⎝⎜⎞⎠⎟⎡⎣⎢⎢⎤⎦⎥⎥=−⎛⎝⎜⎞⎠⎟−−⎛⎝⎜⎞⎠⎟⎡⎣⎢⎢⎤⎦⎥⎥+−ρμσρμσμσμσμσρμσρqxxxxxx(()−⎛⎝⎜⎞⎠⎟x111 2 μσ.Furthermore,xxx ... follows: 12 1 2 111 2 111 22 2 22 2 2 22 2111 2 2−()=−⎛⎝⎜⎞⎠⎟−−⎛⎝⎜⎞⎠⎟−⎛⎝⎜⎞⎠⎟+−⎛⎝⎜⎞⎠⎟⎡⎣⎢⎢⎤⎦⎥⎥=−⎛⎝⎜⎞⎠⎟−−⎛⎝⎜⎞⎠⎟⎡⎣⎢⎢⎤⎦⎥⎥+−ρμσρμσμσμσμσρμσρqxxxxxx(()−⎛⎝⎜⎞⎠⎟x111 2 μσ.Furthermore,xxx xxxxb 22 2 111 22 22 2 111 2 22 211 12 2111−⎛⎝⎜⎞⎠⎟−−⎛⎝⎜⎞⎠⎟=−−⋅ ⋅−=−+−⎛⎝⎜⎞⎠⎟⎡⎣⎢⎢⎤⎦⎥⎥=−()μσρμσμσσρσμσσμρσμσσ,wherebx=+ ... andqxxxx=−−⎛⎝⎜⎞⎠⎟−−⎛⎝⎜⎞⎠⎟−⎛⎝⎜⎞⎠⎟+−⎛⎝⎜⎞⎠⎟⎡⎣⎢⎢⎤⎦⎥⎥11 2 2111 2 111 22 2 22 2 2 ρμσρμσμσμσwithμ1,μ 2 ∈ޒ. The distribution of X is also called the Bivariate Normaldistribution and the quantitiesμ1,μ 2 ,σ1,σ 2 ,ρ...