GATE DA 2026 Set 1 — Question 63
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Probability & Statistics → Continuous Random Variables → Conditional Distributions (Continuous)
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Question
Let be a random variable that follows distribution. The conditional distribution of the random variable given is the distribution.The value of is __________ . (Answer in integer)
Correct answer
0 to 0
Solution
Given , we have .
The conditional distribution is , so:The covariance between and is:Since , .
Using the law of total expectation:For , the probability density function is symmetric about 0. Thus, the third moment of is:Since , the correlation is also 0:
The conditional distribution is , so:The covariance between and is:Since , .
Using the law of total expectation:For , the probability density function is symmetric about 0. Thus, the third moment of is:Since , the correlation is also 0:
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