GATE CS 2017 Set 1 — Question 19
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Engineering Mathematics → Probability & Statistics → Continuous Distributions
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Question
Let be a Gaussian random variable with mean 0 and variance . Let where is the maximum of and . The median of is ________ .
Correct answer
0 to 0
Solution
Since is a Gaussian random variable with mean 0, its distribution is symmetric about 0, so .The random variable is defined as .
For , both conditions are satisfied ( and ).
Thus, the median of is 0.
- If , .
- If , .
For , both conditions are satisfied ( and ).
Thus, the median of is 0.
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