The following are the description of the distribution function. distribution law. and density function of random variables. which is incorrect?

Question

Options

• ADistribution law can only describe the value rule of discrete random variables
• BThe density function can only describe the value rule of continuous random variables
• CDiscrete random variables have no d1slribulion function
• DDistribution function describes the value rule of random variables

• A
  8% (2)
• B
  17% (4)
• C
  71% (17)
• D
  4% (1)

Explanation

Option C is incorrect because every random variable - discrete or continuous - possesses a distribution function (cumulative distribution function, CDF), defined as F(x) = P(X ≤ x). The CDF is a universal concept that applies to all random variable types, not just continuous ones. Options A and B are both correct statements: the distribution law (probability mass table) applies exclusively to discrete random variables, and the density function applies exclusively to continuous ones - these are the specialized tools for each type. Option D is also correct because the distribution function is precisely the tool that describes value rules for all random variables, making it the most general of the three concepts.

Memory tip: Think of the distribution function (CDF) as the "universal" descriptor - it works for every random variable. The distribution law and density function are the "specialists" for discrete and continuous cases respectively. The trap in this question is confusing "distribution law" (specialist, discrete only) with "distribution function" (universal) - they sound similar but are not the same thing.

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