Answer: Bayes Theorem can only be applied to discrete random variables, such that continuous random variables must be transformed into their discrete equivalents

## Explanation Let's analyze each statement: **Option A: TRUE** For any valid cumulative distribution function (CDF), the limits must satisfy: - F(−∞) = 0 (as x approaches negative infinity) - F(+∞) = 1 (as x approaches positive infinity) This is a fundamental property of CDFs. **Option B: TRUE** CDFs are always non-decreasing functions. This means that as x increases, F(x) either stays the same or increases, but never decreases. This property holds for both discrete and continuous random variables. **Option C: TRUE** For continuous random variables, the probability of any specific value is zero. This is because continuous random variables have probability density functions (PDFs) rather than probability mass functions (PMFs). The probability is defined over intervals, not specific points. So Pr[R = +3.00%] = 0 for a continuous random variable R. **Option D: FALSE** This is the incorrect statement. Bayes Theorem can be applied to both discrete and continuous random variables. For continuous random variables, we use probability density functions in Bayes Theorem: \[f_{X|Y}(x|y) = \frac{f_{Y|X}(y|x) \cdot f_X(x)}{f_Y(y)}\] Where f represents probability density functions. Continuous random variables do NOT need to be transformed into discrete equivalents to apply Bayes Theorem. **Therefore, Option D is the false statement.**

Author: LeetQuiz Editorial Team