Chapter 2 Section 1 Question 11

Question

Suppose the sample space S is finite. Is it possible to define an unbounded random variiable on S? Why or why not?

Answer

Author: Mohammad-Ali Bandzar| Date:Oct 14 2020

we can find the definition of unbounded from Example 2.1.10: if X(s) increases or decreases without bound as $s\rightarrow\infty$ X can be called an unbounded random variable.

If our sample space is finite we can not have an unbounded random variable on S. This is because we must have an upper bound defined by $max_{s\in S}X(s)$ and a lower one defined by: $min_{s\in S}X(s)$.

we can find the definition of unbounded from Example 2.1.10: if X(s) increases or decreases without bound as $s\rightarrow\infty$ X can be called an unbounded random variable.

If our sample space is finite we can not have an unbounded random variable on S. This is because we must have an upper bound defined by $max_{s\in S}X(s)$ and a lower one defined by: $min_{s\in S}X(s)$.