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Let f(x) represent a probability function (which is called a probability mass function, p.m.f., for discrete random variables and a probability density function, p.d.f., for continuous variables) and let F(x) represent the corresponding cumulative distribution function (CDF); in the case of the continuous variable, F(x) is the integral (aka, anti-derivative) of the pdf. Each of the following is true about these probability functions EXCEPT which is false?
A
The limits of a cumulative distribution function (CDF) must be zero and one; i.e., F(−∞) = 0 and F(+∞) = 1.0
B
For both discrete and continuous random variables, the cumulative distribution function (CDF) is necessarily a non-decreasing function.
C
In the case of a continuous random variable, we cannot talk about the probability of a specific value occurring; e.g., Pr[R = +3.00%] is meaningless
D
Bayes Theorem can only be applied to discrete random variables, such that continuous random variables must be transformed into their discrete equivalents