5. (12%) For the following 4 functions, check if you can calculate a constant c

Question

5. (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-x2+2y-y2 a. d. k(x, y)-cety2 6, (1090) Repeat Q5 with functions changed to a. f(x, y) = c e-x2+xy-2y2 b. g(x, y)-c e-*2+xy+2y2 2

Explanation / Answer

5)
only
a) can become a valid pdf
note that as f(x,y) should tend to 0 as x and y tend to infinity

so positive sign befor x^2 or y^2 is not allowed

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