
Answer-first summary for fast verification
Answer: Bernoulli (lowest) and Poisson (highest)
## Explanation Let's calculate the variances for each distribution: 1. **Standard Normal**: Variance = 1 2. **Student's t (df=10)**: Variance = df/(df-2) = 10/8 = 1.25 3. **Bernoulli (p=0.04)**: Variance = p(1-p) = 0.04 × 0.96 = 0.0384 4. **Poisson (λ=5)**: Variance = λ = 5 5. **Binomial (n=50, p=0.02)**: Variance = np(1-p) = 50 × 0.02 × 0.98 = 0.98 **Variance Ranking**: - Lowest: Bernoulli = 0.0384 - Highest: Poisson = 5 Therefore, the correct answer is **Bernoulli (lowest) and Poisson (highest)**, which corresponds to option C. **Verification**: - Bernoulli: 0.0384 (lowest) - Standard Normal: 1 - Binomial: 0.98 - Student's t: 1.25 - Poisson: 5 (highest)
Author: LeetQuiz .
Ultimate access to all questions.
Consider the following five random variables:
Which of the above has, respectively, the lowest value and highest value as its variance among the set?
A
Standard normal (lowest) and Bernoulli (highest)
B
Binomial (lowest) and Student's t (highest)
C
Bernoulli (lowest) and Poisson (highest)
D
Poisson (lowest) and Binomial (highest)
No comments yet.