Problem 6.1 (Video 4.1 - 4.7, Lecture Problem) Let X be Uniform[1, 2]. Let Y given X = x be Exponential(x); that is, fy|x(y|x) = xexy, y ≥ 0 and 0, y < 0. (a) Find the expected value of Y. (Hint: see HW 5, problem 5.4e). (It is OK to leave your answer as an integral.) (b) Find the conditional expected value E[Y|X = x] of Y given X = x. (This should be in closed form.) (c) Using E[Y] = E[E[Y|X]] find the expected value of Y. (This should be in closed form.) (d) Solve for E[XY].
Problem 6.1 (Video 4.1 - 4.7, Lecture Problem) Let X be Uniform[1, 2]. Let Y given X = x be Exponential(x); that is, fy|x(y|x) = xexy, y ≥ 0 and 0, y < 0. (a) Find the expected value of Y. (Hint: see HW 5, problem 5.4e). (It is OK to leave your answer as an integral.) (b) Find the conditional expected value E[Y|X = x] of Y given X = x. (This should be in closed form.) (c) Using E[Y] = E[E[Y|X]] find the expected value of Y. (This should be in closed form.) (d) Solve for E[XY].
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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![Problem 6.1 (Video 4.1 - 4.7, Lecture Problem) Let X be Uniform[1, 2]. Let Y given
X = x be Exponential(x); that is, fy|x(y|x) = xexy, y ≥ 0 and 0, y < 0.
(a) Find the expected value of Y. (Hint: see HW 5, problem 5.4e). (It is OK to leave your
answer as an integral.)
(b) Find the conditional expected value E[Y|X = x] of Y given X = x. (This should be in
closed form.)
(c) Using E[Y] = E[E[Y|X]] find the expected value of Y. (This should be in closed form.)
(d) Solve for E[XY].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02681530-b6ca-4d72-bfd1-7260256101ab%2F10db2274-b43e-43ba-a47b-f2b0716c9722%2Fei7pdk_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 6.1 (Video 4.1 - 4.7, Lecture Problem) Let X be Uniform[1, 2]. Let Y given
X = x be Exponential(x); that is, fy|x(y|x) = xexy, y ≥ 0 and 0, y < 0.
(a) Find the expected value of Y. (Hint: see HW 5, problem 5.4e). (It is OK to leave your
answer as an integral.)
(b) Find the conditional expected value E[Y|X = x] of Y given X = x. (This should be in
closed form.)
(c) Using E[Y] = E[E[Y|X]] find the expected value of Y. (This should be in closed form.)
(d) Solve for E[XY].
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