Explain which of the following functions can be used as probability functions of a random variable X with the corresponding range RX given below:

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x+3 (i) f(x) = Rx = {1,2,3}; 15 2x-3 (ii) f(x) = Rx = {1,2,3,4); 16 3x-1 (iii) f(x) = Rx = {1,2,...); 4 x (iv) f(x)= Ry = {1, 2, ..., n}; n(n + 1)(2n+1)* (v) f(x) = (-1) (10), Rx = {1, 2,..., 10}; -n(n), Ry = {0,1,2,...,) (vi) f(x) = 2" (").