21 Let (X₁, X₂) be jointly continuous random vector with the following information: you are given the conditional density of X₁ given X₂ and the marginal density of X₂. and fx₁|x₂(x₁|x₂) = C121 x² 0 fx₂(x₂) = " 0
21 Let (X₁, X₂) be jointly continuous random vector with the following information: you are given the conditional density of X₁ given X₂ and the marginal density of X₂. and fx₁|x₂(x₁|x₂) = C121 x² 0 fx₂(x₂) = " 0
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.7: More On Inequalities
Problem 44E
Related questions
Question
Could you please explain to me how to do question 1 in hand?
I am having so much trouble sketch the support, so could you draw and explain how to draw the graph?
Thank you
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step 1: Write the given information
VIEWStep 2: Sketch the support of (X1 and X2) and find the constant c1 and c2
VIEWSolution
VIEWStep 3: Determine the joint probability density function of X1 and X2
VIEWStep 4: Determine the marginal density function of X1
VIEWStep 5: Find E[X1] and E[X2]
VIEWStep 6: Find the conditional density of X2 given X1=x1 and the conditional expectation of X1 given X2=x2
VIEWStep 7: What is E[X₁|X₂] and veify that E[X₁] is the same as the one obtained in part Q1 (iv.)
VIEWStep 8: Find E[X1] using the joint density directly and verify that it is the same as obtained above
VIEWStep 9: Find E[X1-X2], using the joint density directly
VIEWStep 10: Find EX1 X2], using the joint density directly and Find the Cov(X1, X2)
VIEWStep by step
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