When rolled, a die fails to turn up with equal probabilities for each of the six possibilities because it has been damaged. A large number of rolls of this die confirms that one dot and four dots appear with probability 1/5; two, three and six dots with probability 1/10; and five dots with probability 3/10. Let D denote the absolute value of the difference of dots that show when this die is rolled two times.
Q: Write down its probability density function (p.d.f.) and its cumulative distribution function