Answer:
76
Step-by-step explanation:
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<em>Y</em>₁ and <em>Y</em>₂ are independent, so their joint density is

By definition of conditional probability,
P(<em>Y</em>₁ > <em>Y</em>₂ | <em>Y</em>₁ < 2 <em>Y</em>₂) = P((<em>Y</em>₁ > <em>Y</em>₂) and (<em>Y</em>₁ < 2 <em>Y</em>₂)) / P(<em>Y</em>₁ < 2 <em>Y</em>₂)
Use the joint density to compute the component probabilities:
• numerator:






• denominator:

(I leave the details of the second integral to you)
Then you should end up with
P(<em>Y</em>₁ > <em>Y</em>₂ | <em>Y</em>₁ < 2 <em>Y</em>₂) = (1/6) / (2/3) = 1/4
The common denominator is 1
Given the expression:
Find the LCM of the numerator to have:
Simplify both the numerator and the denominator to have:

From the result, we can see that the common denominator is 1
Learn more about fractions here: brainly.com/question/17743912