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If the joint density of X and Y was uniform on the region 0 < x...

If the joint density of X and Y was uniform on the region 0 < x < 1 and 0 < y < 2 − 2x, find the probability P(2X − Y < 0).

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Answer #1

The joint PDF is

Where is the area of the triangular region

Consider the figure below.

The area of the triangular region is .

Thus, the joint PDF is

The area of the shaded region (in rose) is  .

Thus the required probability is

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