1.5 Let Y, and Y2 have the joint probability density function given by 0 < y1 < y2 S1 elsewhere 0, 1.5.1 If k = 6, show that it makes f(V1,Y2) a joint probability density function. 1.5.2 The marginal densities for Y, and Y2 are found to be fi (y1) = 3(1 – yı)? and f2(y2) = 6y2(1- y2) respectively. In your own words explain how these marginal densities were obtained. 1.5.3 Identify the distribution of f2 (y2). 1.5.4 Show that f(yıly2) =. Y2 1.5.5 Motivate or show whether Y, and Y2 are dependent or independent.
1.5 Let Y, and Y2 have the joint probability density function given by 0 < y1 < y2 S1 elsewhere 0, 1.5.1 If k = 6, show that it makes f(V1,Y2) a joint probability density function. 1.5.2 The marginal densities for Y, and Y2 are found to be fi (y1) = 3(1 – yı)? and f2(y2) = 6y2(1- y2) respectively. In your own words explain how these marginal densities were obtained. 1.5.3 Identify the distribution of f2 (y2). 1.5.4 Show that f(yıly2) =. Y2 1.5.5 Motivate or show whether Y, and Y2 are dependent or independent.
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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![1.5 Let Y, and Y2 have the joint probability density function given by
FU1Y2) = {"0.
1-y2),
0 < y1 < y2 <1
elsewhere
%3D
1.5.1 If k = 6, show that it makes f(y1Y2) a joint probability density function.
1.5.2 The marginal densities for Y, and Y2 are found to be fi (y1) = 3(1 – yı)?
and f2(y2) = 6y2(1– y2) respectively. In your own words explain how these marginal
densities were obtained.
1.5.3 Identify the distribution of f2(y2).
1.5.4 Show that fVi\y2) =.
Y2
1.5.5 Motivate or show whether Y, and Y2 are dependent or independent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9decaac-d845-4b51-b943-714ca4810fbe%2Fa493065d-943f-4584-809a-2e76330e0d2b%2Fg2oe2w9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1.5 Let Y, and Y2 have the joint probability density function given by
FU1Y2) = {"0.
1-y2),
0 < y1 < y2 <1
elsewhere
%3D
1.5.1 If k = 6, show that it makes f(y1Y2) a joint probability density function.
1.5.2 The marginal densities for Y, and Y2 are found to be fi (y1) = 3(1 – yı)?
and f2(y2) = 6y2(1– y2) respectively. In your own words explain how these marginal
densities were obtained.
1.5.3 Identify the distribution of f2(y2).
1.5.4 Show that fVi\y2) =.
Y2
1.5.5 Motivate or show whether Y, and Y2 are dependent or independent.
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