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7. Suppose that X and Y have a continuous joint distribu- tion for which the joint p.d.f. is as follows: fr. y) = [x+y for 0<1<1 and 0< y<1, otherwise. Find E(Y|X) and Var(Y|X).

7. Suppose that X and Y have a continuous joint distribu- tion for which the joint p.d.f. is as follows: fr. y) = [x+y for 0<1<1 and 0< y<1, otherwise. Find E(Y|X) and Var(Y|X).

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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answer for question 10. Also i marked excercise 7 and 9

15. Con student 6. Suppose that the joint distribution of X and Y is the uni- form distribution on the circle x? + y? < 1. Find E(X]Y). 7. Suppose that X and Y have a continuous joint distribu- tion for which the joint p.d.f. is as follows: dicted v M.S.E. what pr has the Įx+y for 0 <x<l and 0< y <1, fx. y) = 16. Den otherwise. any me x. Supp need to Find E(Y|X) and Var(Y|X). 8. Consider again the conditions of Exercise 7. (a) If it is observed that X = 1/2, what predicted value of Y will have the smallest M.S.E.? (b) What will be the value of this M.S.E.? predicti E(|Y – a condi modify 9. Consider again the conditions of Exercise 7. If the value of Y is to be predicted from the value of X, what will be the minimum value of the overall M.S.E.? 17. Pro have a to write 10 Suppose that, for the conditions in Exercises 7 and 9, a person either can pay a cost e for the opportunity of observing the value of X before predicting the value of Y the joir facilitat values s
Transcribed Image Text:15. Con student 6. Suppose that the joint distribution of X and Y is the uni- form distribution on the circle x? + y? < 1. Find E(X]Y). 7. Suppose that X and Y have a continuous joint distribu- tion for which the joint p.d.f. is as follows: dicted v M.S.E. what pr has the Įx+y for 0 <x<l and 0< y <1, fx. y) = 16. Den otherwise. any me x. Supp need to Find E(Y|X) and Var(Y|X). 8. Consider again the conditions of Exercise 7. (a) If it is observed that X = 1/2, what predicted value of Y will have the smallest M.S.E.? (b) What will be the value of this M.S.E.? predicti E(|Y – a condi modify 9. Consider again the conditions of Exercise 7. If the value of Y is to be predicted from the value of X, what will be the minimum value of the overall M.S.E.? 17. Pro have a to write 10 Suppose that, for the conditions in Exercises 7 and 9, a person either can pay a cost e for the opportunity of observing the value of X before predicting the value of Y the joir facilitat values s
ple or can simply predict the value of Y without first observing dict the value of X. If the person considers her total loss to be han the cost e plus the M.S.E. of her predicted value, what is the maximum value of c that she should be willing to pay? a 11. Prove Theorem 4.74.
Transcribed Image Text:ple or can simply predict the value of Y without first observing dict the value of X. If the person considers her total loss to be han the cost e plus the M.S.E. of her predicted value, what is the maximum value of c that she should be willing to pay? a 11. Prove Theorem 4.74.
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