Consider the random experiment of casting two dice and counting the total number of dots appearing on the uppermost faces. The random variable X takes the value 0 when the total number of dots is odd and 1 when the total number of dots is even.

(a) Derive the density function of the random variable X assuming that the two dice are symmetric.

(b) Derive the density function of the random variable X assuming that the two dice are non-symmetric.