P(x=1) = 1/15; P(x=2) = 2/15; P(x=3) = 3/15; P(x=4) = 4/15; P(x=5) = 5/15

b. For a distribution of probabilities to be valid, they must meet three requirements: the probability sum must equal 1, and every value must be unique (no more than two values may have the same chance).

This is the case when x’s probability distribution meets certain conditions. As fractions, all probabilities in this distribution are either greater than or equal 0 because they have numerators of no more than 5, and denominators of 15. Furthermore, when we add up all five of these fractions (1/15 + 2/15 + 3/15 + 4/15 + 5 / 15), we get an answer of 15 / 15 which simplifies to 1 – meaning that the sum of all probabilities in this distribution does indeed equal 1.

Finally, each value has a unique probability – none of them share any similarities or ratios between them which would indicate that they could be combined into one collective fraction. It follows that the discrete probabilities distribution we have created has all of the required properties for mathematicians to accept it as valid.