Continuous random variables X and Y have the following joint PDF:In x²,f(x, y)-1 ≤ x ≤ 1,0 ≤ y ≤ x²otherwise.Let the event A = {Y ≤ 0.36}.Find the conditional PDF (and the range) of Y given A and the expectedvalue of Y given A. Please provide the solution step by step.

Let X and Y have a joint density function

Answered: In x², f(x, y) = ») - 0, -1 ≤x≤1, 0≤ y…

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In x², f(x, y) = ») - 0, -1 ≤x≤1, 0≤ y ≤ x² otherwise. Let the event A = {Y ≤ 0.36}. Find the conditional PDF (and the range) of Y given A and the expected value of Y given A. Please provide the solution step by step.