Question

Consider the following probability distributions. Which of the following are continuous probability distributions?
(A). Normal distribution
(B). Binomial distribution
(C). Poisson distribution
(D). Chi-square distribution
(E). F-distribution

Choose the correct answer from the options given below:

• A. (B) and (C) only.
• B. (A), (B) and (C) only.
• C. (A), (D) and (E) only.
• D. (D) and (E) only.

Hint:

Remember that Binomial and Poisson distributions deal with integers and discrete counts of events, which immediately classifies them as discrete.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Probability distributions are classified as either discrete or continuous depending on the type of random variable they model.
A discrete distribution models countable outcomes, whereas a continuous distribution models outcomes over an uninterrupted interval.

Step 3: Detailed Explanation:
Let us categorize each distribution listed:
(A)

Normal distribution: A continuous distribution that forms a symmetric bell-shaped curve.
(B)

Binomial distribution: A discrete distribution representing the number of successes in a fixed number of independent trials.
(C)

Poisson distribution: A discrete distribution representing the count of events occurring within a specified interval.
(D)

Chi-square distribution: A continuous distribution widely used in hypothesis testing, which is the distribution of a sum of squares of independent standard normal variables.
(E)

F-distribution: A continuous distribution representing the ratio of two scaled chi-square variables.
Thus, (A), (D), and (E) are continuous probability distributions.

Step 4: Final Answer:
The correct option is 3, which corresponds to (A), (D) and (E) only.