Question
Download Solution PDFLet X be uniform random variable on [0, 4] and Y be uniform random variable on [0, 1]. If X and Y are independent, then P(max{X, Y} > 3) is equal to:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is ption 1: 1/4
Key Points
We are given:
- X ~ Uniform(0, 4)
- Y ~ Uniform(0, 1)
- X and Y are independent
We are asked to find:
Note:
But since Y ~ Uniform(0, 1), it always satisfies Y ≤ 3. So, the event
So,
Since X ~ Uniform(0, 4),
Therefore,
Correction: The correct value is 1/4, so the correct answer is:
option 1: 1/4
Additional Information
- The maximum of two variables exceeds a threshold if at least one exceeds it.
- Since Y ∈ [0,1], and 1 < 3, the only contributing factor is whether X > 3.
- P(X > 3) = (4 − 3) / (4 − 0) = 1/4
Hence, the correct answer is: option 1: 1/4
Last updated on Jul 3, 2025
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