Let the event A = {Y ≤ 0.36}. Find the conditional PDF (and the range) of Y given A and the expecte value of Y given A. Please provide the solution step by step.

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Continuous random variables X and Y have the following joint PDF:
£2.5 x²,
10,
f(x, y) =
-1 ≤x≤1, 0≤ y ≤r²
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.
Transcribed Image Text:Continuous random variables X and Y have the following joint PDF: £2.5 x², 10, f(x, y) = -1 ≤x≤1, 0≤ y ≤r² 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.
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Follow-up Question

i think in step 3 marginal of pdf y is wrong because of y's range is wrong.
in the question -1<= x <= 1 and 0 <= y <= x^2. 
could you check?

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