Question

1. the distribution of a random variable is symmetric. which of the following statements is guaranteed to be true? a) the variable is a continuous random variable. b) the median is less than the mean. c) the distribution is normal. d) the distribution is uniform. e) none of the above.

Explanation:

• Option A: Symmetric distributions can apply to discrete random variables (e.g., binomial distribution with p=0.5), so this is not guaranteed.
• Option B: For symmetric distributions, the mean equals the median, so this is false.
• Option C: Many symmetric distributions are not normal (e.g., uniform distribution, discrete symmetric binomial), so this is not guaranteed.
• Option D: There are non-uniform symmetric distributions (e.g., normal distribution, symmetric binomial), so this is not guaranteed.

Answer:

E) None of the above.