For each of the following functions, does a constant c > 0 exist such that the...

For each of the following functions, does a constant c > 0 exist such that the function is a joint probability density function?

If yes, what is c? If not, why not?

Part (a) gives 2 points, parts (b)–(d) give each one point.

(a) f(x, y) = ( cxye −x−2y if x ≥ 0 and y ≥ 0, 0 otherwise.

(b) f(x, y) = ( cxye −x−2y if x ≥ −1 and y ≥ 1, 0 otherwise.

(c) f(x, y) = ( e −cxy if x ≥ 0 and y ≥ 1, 0 otherwise.

(d) f(x, y) = ( 1 y e −cxy if x ≥ 0 and y ≥ 1, 0 otherwise.

Expert Solution

orchestra answered 1 year ago

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