Give an example of a discrete distribution and a continuous distribution.

Give an example of a discrete distribution and a continuous distribution.

• A. Discrete: Poisson; Continuous: Exponential
• B. Discrete: Uniform; Continuous: Cauchy
• C. Discrete: Binomial; Continuous: Normal
• D. Discrete: Normal; Continuous: Binomial

Answer: (C)

The main idea is distinguishing discrete from continuous distributions. A discrete distribution assigns probability to specific, countable outcomes; the Binomial distribution is a classic example—counting the number of successes in n independent trials with two outcomes, so its possible values are the integers 0 through n. A continuous distribution assigns probability to intervals on a continuum; the Normal distribution has a density defined for every real number, so probabilities come from ranges, not individual points. This pairing—Binomial for the discrete side and Normal for the continuous side—is a clear, standard illustration because it contrasts a countable set of outcomes with a smooth density over all real numbers. Other options either label a distribution in a nonstandard way (Uniform is typically continuous on an interval) or mix types in a way that isn’t the common textbook pairing, even though other discrete-continuous pairs (like Poisson with Exponential) exist.

The main idea is distinguishing discrete from continuous distributions. A discrete distribution assigns probability to specific, countable outcomes; the Binomial distribution is a classic example—counting the number of successes in n independent trials with two outcomes, so its possible values are the integers 0 through n. A continuous distribution assigns probability to intervals on a continuum; the Normal distribution has a density defined for every real number, so probabilities come from ranges, not individual points. This pairing—Binomial for the discrete side and Normal for the continuous side—is a clear, standard illustration because it contrasts a countable set of outcomes with a smooth density over all real numbers. Other options either label a distribution in a nonstandard way (Uniform is typically continuous on an interval) or mix types in a way that isn’t the common textbook pairing, even though other discrete-continuous pairs (like Poisson with Exponential) exist.