Asked by Khizar Rehman on Sep 28, 2024
Verified
If the random variable X is exponentially distributed,then the mean of X will be:
A) greater than the median.
B) less than the median.
C) equal to the median.
D) Cannot tell; the answer depends on what λ is.
Exponential Distribution
A statistical distribution that characterizes the interval between occurrences in a scenario where events happen constantly and independently, maintaining a uniform average frequency.
- Compute the central tendencies and measures of variability, specifically mean, median, variance, and standard deviation, for exponential distributions.
Verified Answer
CH
Chris Hicksabout 11 hours ago
Final Answer :
A
Explanation :
The mean of an exponentially distributed random variable X is equal to 1/λ, while the median is equal to ln(2)/λ. Since ln(2) is less than 1, the median is greater than the mean, so the answer is A.
Learning Objectives
- Compute the central tendencies and measures of variability, specifically mean, median, variance, and standard deviation, for exponential distributions.
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