Problem 5.5 (Video 4.1 - 4.5, Lecture Problem) You are manufacturing parts that have quite a bit of variability in their quality. Let us model this by saying X is Uniform[1,2]. The lifetime of a part is modeled by Y, and we know that Y given X = x is Exponential(x). (a) Are X and Y independent? (b) What is the joint PDF fx,y(x, y)? (c) Calculate P[Y < 1].
Problem 5.5 (Video 4.1 - 4.5, Lecture Problem) You are manufacturing parts that have quite a bit of variability in their quality. Let us model this by saying X is Uniform[1,2]. The lifetime of a part is modeled by Y, and we know that Y given X = x is Exponential(x). (a) Are X and Y independent? (b) What is the joint PDF fx,y(x, y)? (c) Calculate P[Y < 1].
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Only a, b, c please!! Thank you!!!
![Problem 5.5 (Video 4.1 - 4.5, Lecture Problem) You are manufacturing parts that have
quite a bit of variability in their quality. Let us model this by saying X is Uniform[1, 2]. The
lifetime of a part is modeled by Y, and we know that Y given X = x is Exponential(x).
(a) Are X and Y independent?
(b) What is the joint PDF fx,y(x, y)?
(c) Calculate P[Y < 1].
(d) Determine the marginal PDF fy(y).
(e) Find the expected value of Y using fy(y).
(f) What is E[X + Y]? (This should be in closed form.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02681530-b6ca-4d72-bfd1-7260256101ab%2Fe37728c7-2504-4dbf-8013-f8064f03e93f%2Fufl3i7p_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 5.5 (Video 4.1 - 4.5, Lecture Problem) You are manufacturing parts that have
quite a bit of variability in their quality. Let us model this by saying X is Uniform[1, 2]. The
lifetime of a part is modeled by Y, and we know that Y given X = x is Exponential(x).
(a) Are X and Y independent?
(b) What is the joint PDF fx,y(x, y)?
(c) Calculate P[Y < 1].
(d) Determine the marginal PDF fy(y).
(e) Find the expected value of Y using fy(y).
(f) What is E[X + Y]? (This should be in closed form.)
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