Final answer:
A random variable X is considered a constant if it takes on a single value for all outcomes. X:Ω→R is proven to be a random variable if X is constant.
Step-by-step explanation:
In mathematics, a random variable X is considered a constant if it takes on a single value for all outcomes in the sample space Ω. In other words, the value of X does not change and is not affected by the outcomes of the experiment. Let's prove that X:Ω→R is a random variable if X is constant.
a. The random variable X is defined as constant, which means it takes on a single value for all outcomes.
b. The value that X may take on is this single constant value.
c. The distribution of X can be represented as a single point on the number line. X~ is a degenerate distribution.