(All Steps) Let Y 1 and Y 2 denote the proportions of two different types of components in a sample from a mixture of chemicals used as an insecticide. Suppose


Question: Let Y 1 and Y 2 denote the proportions of two different types of components in a sample from a mixture of chemicals used as an insecticide. Suppose that Y 1 and Y 2 have the joint density function given by:

f(y 1 ,y 2 )= 2, 0 ≤ y 1 ≤ 1, 0 ≤ y 2 ≤ 1, 0 ≤ y 1 + y 2 ≤ 1,

0, elsewhere

(Notice that Y 1 + Y 2 ≤ 1 because the random variables denote proportions within the same sample.) Find:

  1. P(Y 1 ≤ ¾, Y 2 ≤ ¾).
  2. P(Y 1 ≤ ½, Y 2 ≤ ½).

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