3. Consider two random variables X₁ and X₂ whose joint pdf is given by 11/2 for x₁ > 0, x2 > 0, x1 + x₂ < 2, { otherwise. f(x1, x2) = Find the pdf of Y=X2-X₁. 0

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A: The P.D.F is given by: fx=ddxFx=ddxcx-14=4cx-13

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A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

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A: As per bartleby guidelines we can solve only first question and rest can be reposted

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A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

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A: Step 1: Step 2: Step 3: Step 4:

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A: Here Marginal pdf of X1 = f(x1) =f(x1)=∫01f(x1,x2) dx2 =∫0112x1x2(1-x2) dx2 =∫0112x1(x2-x22)dx2…

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A: Given that, V(X)= V(Y)= 1 So  V(Z) = V(X+bY)  = V(X)+b2V(Y)  { x and Y are independent} = 1+ b2

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