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  3. (12%) for the following 4 functions, check if you

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

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Advance Math

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