X is a random variable that has two different distributions, f (X) and g(x).

f(x) is presented in the following table, while g(x) is defined as g(X) = (2X + 1) ²

a) Determine g(X) for each value of the random variable X.

b) Determine whether each of f(X) or g(X) can be a probability distribution. Explain.

c) Find the average ?f(x) and the standard deviation. ?f(x) relative to f (X).

X f(x) g(x) -3 1/6 6 1/2 9 1/3