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