GATE CE 2023 Set 1 — Question 7
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Engineering Mathematics → Probability → Mean, Median & Mode
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Question
Which one of the options can be inferred about the mean, median, and mode for the given probability distribution (i.e. probability mass function), , of a variable ?
Correct answer
(A) mean = median ≠ mode
Solution
The given probability distribution is symmetric about the vertical axis at . For any symmetric distribution, the mean and median are equal and located at the center of symmetry. Thus, . The mode is the value of at which the probability mass function attains its maximum value. In this bimodal distribution, there are two peaks of equal height at and . Therefore, the modes are . Since the modes are not equal to the mean and median, the correct relationship is .
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