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For each of the following functions, determine the constant c so that f(x, y) satisfies the conditions of being a joint pmf for two discrete random variables X and Y: (a) f(x, y) = c(x + 2y), x = 1, 2, y = 1, 2, 3. (b) f(x, y) = c(x + y), x = 1, 2, 3, y = 1, ... , x. (c) f(x, y) = c, x and y are integers such that 6 ≤ x+y ≤ 8, 0 ≤ y ≤ 5. (d) f(x, y) = c 1 4 x1 3 y , x = 1, 2, ... , y = 1, 2, ... .
Sagot :
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