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)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb185c4f8-45fd-4a32-b444-93e3110a115d%2F759fba57-b8db-474d-88d6-0bf4d3edade1%2F1f95q9s_processed.jpeg&w=3840&q=75)
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
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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