Question

Let Y₁ and Y₂ have the joint density function. Find the probability (Y₁ - Y₂ > 1/2).

Answer 1

To find the probability that Y₁ - Y₂ > 1/2, you need to determine the joint density function of Y₁ and Y₂ and then integrate the joint density function over the region Y₁ - Y₂ > 1/2.

Step-by-step explanation:

To find the probability that Y₁ - Y₂ > 1/2, we need to determine the joint density function of Y₁ and Y₂.

1. Start by finding the cumulative distribution function (CDF) of Y₁ and Y₂ separately.
2. Then, use the joint density function to find the probability of Y₁ and Y₂ being in a certain range.
3. Finally, integrate the joint density function over the region Y₁ - Y₂ > 1/2 to find the desired probability.