If Y 1 and Y 2 are continuous random variables with joint density function f(y 1 , y 2 ) 6(1 y 2 ), 0 y 1 y 2 1, find (a) f 1 (y 1 ) and (b) P(Y 2 1 2 Y 1 3 4) and (c) P (Y 2 3 4 Y 1 1 2) Ans (a) f 1 (y 1 ) 3(1 y 1 )2, 0 y 1 1 (b) 32 63 (c) 1 4

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Question: If Y 1 and Y 2 are continuous random variables with joint density function f(y 1 , y 2 ) = 6(1 y 2 ),

If Y₁ and Y₂ are continuous random variables with joint density function f(y₁, y₂) = 6(1 y₂), 0 y₁ y₂ 1, find (a) f₁(y₁) and (b) P(Y₂ 1/2 | Y₁ 3/4) and (c) P (Y₂ 3/4 | Y₁ = 1/2). Ans. (a) f₁(y₁) = 3(1 y₁)2, 0 y₁ 1 (b) 32/63 (c) 1/4

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