a) see table below
b) mean probability of the distribution is 3.5
Step-by-step explanation:
a) For a fair die, we have an equal chance of getting each of the numbers
Since the count of the numbers = 6
Probability of one of the numbers = 1/6
constructing a table representing the probability:
let x = 1, 2, 3, 4, 5, 6
P(x) = probability of each of the numbers occurring
b) To get the mean of the distribution, we will multiply x by P(x) for each of the numbers. Then we will sum together.
![\begin{gathered} \operatorname{mean}\text{ = }\sum ^{}_{}x(Px) \\ \operatorname{mean}\text{ = }(1)/(6)(1)\text{ + }(1)/(6)(2)\text{ + }(1)/(6)(3)\text{+ }(1)/(6)(4)\text{+ }(1)/(6)(5)\text{+ }(1)/(6)(6) \\ \operatorname{mean}\text{ = }(1)/(6)(1\text{ + 2 + 3 + 4 + 5 + 6)} \\ \operatorname{mean}\text{ = }(1)/(6)(21) \\ \operatorname{mean}\text{ = 3.5} \end{gathered}]()
mean probability of the distribution is 3.5