What does it mean to say that the real-valued RVs X and Y are inde- pendent, and how, in terms of the joint PDF fx.y could you recognise whether X and Y are independent? The non-negative RVs X and Y...

What does it mean to say that the real-valued RVs X and Y are inde-<br>pendent, and how, in terms of the joint PDF fx.y could you recognise whether X and Y<br>are independent? The non-negative RVs X and Y have the joint PDF<br>Sx.y(x, y) =;(x+y)e-+») (x, y > 0), x, yɛ R.<br>Find the PDF fy and hence deduce that X and Y are not independent. Find the joint PDF<br>of (1X, tY ), where t is a positive real number. Suppose now that T is an RV independent<br>of X and Y with PDF<br>21, if 0<t<1<br>p(1) =<br>%3D<br>0,<br>otherwise.<br>Prove that TX and TY are independent.<br>

Extracted text: What does it mean to say that the real-valued RVs X and Y are inde- pendent, and how, in terms of the joint PDF fx.y could you recognise whether X and Y are independent? The non-negative RVs X and Y have the joint PDF Sx.y(x, y) =;(x+y)e-+») (x, y > 0), x, yɛ R. Find the PDF fy and hence deduce that X and Y are not independent. Find the joint PDF of (1X, tY ), where t is a positive real number. Suppose now that T is an RV independent of X and Y with PDF 21, if 0<><1 p(1)="%3D" 0,="" otherwise.="" prove="" that="" tx="" and="" ty="" are="">

Jun 11, 2022

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What does it mean to say that the real-valued RVs X and Y are inde- pendent, and how, in terms of the joint PDF fx.y could you recognise whether X and Y are independent? The non-negative RVs X and Y...

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