Joe Smith is a contractor who owns his own business In a typ

Joe Smith is a contractor who owns his own business. In a typical month, the number of contracts that he gets varies according to the following distribution: Number of contracts 8 7 6 5 Probability 0.20 0.30 0.40 0.10 What distribution best represents simulating the number of contracts in a given month? Select one: a. discrete uniform b. continuous uniform c. normal d. triangular e. custom

Solution

D.

Probability of contracts first increase from 0.2 to 0.4 (peak) then decrease to 0.10 simply shows a triangle shape discrete function starting from 0.2 to increasing to 0.4 & return to 0.3 shows a triangular uniform distribution.

The given probability distribution function p(x) is accurately fitted into triangular probability function which is 2(x-a)/(b-a)(c-a) when x is greater than or equal to a and less than or equal to c.

P(x) equal to 2(b-x)/(b-a)(b-c) when x is greater than c and less than or equal to b.

Hence this is an triangular uniform function,

Option D is correct.