A warranty is provided for a product worth 10,000 such that the buyer is given 8,000 if it fails in the first year, 6,000 if it fails in the second year, 4,000 if it fails in the third year, 2,000 if it fails in the fourth year and zero after that. The probability of failure in a year is 0.1. Payments are only received at the first failure. The random variable X is the number of years before the first failure occurs.

(i) Determine the distribution of the random variable X, including the value of the parameter of interest, justifying your answer and stating any assumptions.