Final answer:
The characteristic function (CHF) of a random variable (RV) always exists.
Step-by-step explanation:
The characteristic function (CHF) of a random variable (RV) is defined as the expected value of e^(itX), where X is the random variable and t is a real number. To prove that the characteristic function of a RV always exists, we can use the fact that the expected value of the absolute value of e^(itX) is bounded by the expected value of 1, which is 1. This implies that the characteristic function is integrable for all real values of t. Therefore, the characteristic function of a RV always exists.