Ⓒ suppose the joint probability density function of X / Y given; (nty) for x ≥ 0 / f (x,y) elsewhere that 2 new random v

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Suppose The Joint Probability Density Function Of X Y Given Nty For X 0 F X Y Elsewhere That 2 New Random V 1 (151.74 KiB) Viewed 14 times

Ⓒ suppose the joint probability density function of X / Y given; (nty) for x ≥ 0 / f (x,y) elsewhere that 2 new random variables are defined as follows: Z₁ X + Y Suppose Z2 = = = X X + Y O Then, Show that x = Z₁ Z₂ Y = Z₁ (1-Z₁₂) Next, use the results above to find the joint probability density function, f(Z₁, Z₂). Solution formula Note s ₂) and → Suppose X₁ X₂ has joint density function f(2₁, if Y₁ 1/3 Y₂ are defined by Y₁ = V₁ (X₁, X₂ ) ² Y₂ = U₂ (X₁, X₂), then steps to find new joint probability density function of Yık Y₂ given as followis : Lets X₁ X₂ = W₂ (₁₁) Find J, where I is defined as aw, (y₁ y₂) ayı X₂ be the subjects, therefore X₁ = W₁ (Y₁, Y₂) and Y₂) 2w₂ (y₁, y₂) ayı awi (y₁, y₂) дуг y 20 Əw₂ (y₁, y₂) 2 ƏY= 3 The joint probability density function * |ab|= ad-bc c d f(y₁, y₂) = f [w, (y₁ - y₂), W₂ (y₁ - y₂)]• [131] 2