Let Y1 and Y2 denote the proportions of two different types of components in a sample from a mixture of chemicals used as an insecticide. Suppose that Y1 and Y2 have the joint density function given by 2, 0< yı < 1, 0 < y2 < 1, 0 < y1 + y2 3 1 (0, elsevhere fU1,y2) = %3D (Notice that Y1 + Y2 <1 because the random variables denote proportions within the same sample.) Find P(Y1 < 3/4, Y2 < 3/4) P(Y1 < 1/2, Y2 < 1/2)

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Let Y1 and Y2 denote the proportions of two different types of components in a sample from a mixture
of chemicals used as an insecticide. Suppose that Y1 and Y2 have the joint density function given by
2, 0syı s 1, 0 < y2 < 1, 0 < y1 + y2 < 1
0, elsewhere
fV1,y2) =
(Notice that Y1+Y2 < 1 because the random variables denote proportions within the same sample.) Find
P(Y1 < 3/4, Y2 < 3/4)
P(Y1 < 1/2, Y2 < 1/2)
Transcribed Image Text:Let Y1 and Y2 denote the proportions of two different types of components in a sample from a mixture of chemicals used as an insecticide. Suppose that Y1 and Y2 have the joint density function given by 2, 0syı s 1, 0 < y2 < 1, 0 < y1 + y2 < 1 0, elsewhere fV1,y2) = (Notice that Y1+Y2 < 1 because the random variables denote proportions within the same sample.) Find P(Y1 < 3/4, Y2 < 3/4) P(Y1 < 1/2, Y2 < 1/2)
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