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Let X denote the diameter of an armored electric cable and Y denote the diameter of the ceramic mold that makes the cable. Both X and Y are scaled so that they range between 0 and 1. Suppose that X and Y have the joint density 1 0 < x < y < 1 f(x,y) y = elsewhere (a) Determine if X and Y are independent. (b) Find P(X + Y > 1/2). Figure 0.1: Hint1: the blue area is 0 < x < y < 1 and the green area is x+y> 1/2. The overlapping region (domain of integration) is a quadrilateral. It is a little bit hard to integrate. Y 0 / X Figure 0.2: Hint2: the blue area is 0 < x < y < 1 and the green area is x + y < 1/2. The overlapping region (domain of integration) is a triangle. У 0

Let X denote the diameter of an armored electric cable and Y denote the diameter of the ceramic mold that makes the cable. Both X and Y are scaled so that they range between 0 and 1. Suppose that X and Y have the joint density 1 0 < x < y < 1 f(x,y) y = elsewhere (a) Determine if X and Y are independent. (b) Find P(X + Y > 1/2). Figure 0.1: Hint1: the blue area is 0 < x < y < 1 and the green area is x+y> 1/2. The overlapping region (domain of integration) is a quadrilateral. It is a little bit hard to integrate. Y 0 / X Figure 0.2: Hint2: the blue area is 0 < x < y < 1 and the green area is x + y < 1/2. The overlapping region (domain of integration) is a triangle. У 0

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter65: Achievement Review—section Six
Section: Chapter Questions
Problem 41AR: Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places...
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Let X denote the diameter of an armored electric cable and Y denote the diameter of the ceramic mold that makes the cable. Both X and Y are scaled so that they range between 0 and 1. Suppose that X and Y have the joint density
Transcribed Image Text:Let X denote the diameter of an armored electric cable and Y denote the diameter of the ceramic mold that makes the cable. Both X and Y are scaled so that they range between 0 and 1. Suppose that X and Y have the joint density
1 0 < x < y < 1 f(x,y) y = elsewhere (a) Determine if X and Y are independent. (b) Find P(X + Y > 1/2). Figure 0.1: Hint1: the blue area is 0 < x < y < 1 and the green area is x+y> 1/2. The overlapping region (domain of integration) is a quadrilateral. It is a little bit hard to integrate. Y 0<xy<1 x+y> / X Figure 0.2: Hint2: the blue area is 0 < x < y < 1 and the green area is x + y < 1/2. The overlapping region (domain of integration) is a triangle. У 0<xy< x + y</ x
Transcribed Image Text:1 0 < x < y < 1 f(x,y) y = elsewhere (a) Determine if X and Y are independent. (b) Find P(X + Y > 1/2). Figure 0.1: Hint1: the blue area is 0 < x < y < 1 and the green area is x+y> 1/2. The overlapping region (domain of integration) is a quadrilateral. It is a little bit hard to integrate. Y 0<xy<1 x+y> / X Figure 0.2: Hint2: the blue area is 0 < x < y < 1 and the green area is x + y < 1/2. The overlapping region (domain of integration) is a triangle. У 0<xy< x + y</ x
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