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In: Advanced Math

(12%) For the following 4 functions, check if you can calculate a constant c so that...

(12%) For the following 4 functions, check if you can calculate a constant c so that the function is a PDF over the whole plane or state that such c does not exist and the corresponding function is not a PDF (state the reason for that). Note the signs of the coefficients of x2 and y2 are all different). You do not have to calculate the constant c; just provide reasoning for if that exists or not.

f(x, y) = c e^(-x^2+xy-y^2 )

g(x, y) = c e^(-x^2+xy+y^2 )

h(x, y) = c e^(x^2+xy-y^2 )

k(x, y) = c e^(x^2+xy+y^2 )

f(x, y) = c e^(-x^2+xy-2y^2 )

g(x, y) = c e^(-x^2+xy+〖2y〗^2 )

h(x, y) = c e^(x^2+xy-2y^2 )

k(x, y) = c e^(x^2+xy+〖2y〗^2 )

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Expert Solution

Colby Messinger answered 2 years ago
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