Question

You roll a six-faced dice and observe the number of dots on the top face.

(a) Specify the appropriate sample space S of the random experiment.

(b) Give an example of a partition of S. (Proof is unnecessary.)

(c) Give an example of a probability mass function (pmf) for S.

Answer 1

a) Sample Space: All possible outcomes of rolling a six-faced dice experiment. As in dice rolling experiment 6 outcomes are possible i.e. 1,2,3,4,5 and 6. The sample space is given as follows:

S = {1, 2, 3, 4, 5, 6}

b) Partition of sample space:  

A set of events E1, E2, …, En is said to represent a partition of the sample space S if

Example: Two events E = { set of odd outcomes} = {1, 3, 5} and E' = { set of even outcomes} = {2, 4, 6} are parition of sample space S.

c) Because the die is fair, each of the six faces has an equally likely probability of occurring, i.e., 1/6.

The probability distribution for X can be defined by a so-called probability mass function (pmf) p(x), is given in the table given below: