Questions
BU.232.630.W1.SP25 Quiz 1 solutions
Single choice
Consider two random variables: ๐ can take values ( 4 , 5 ) , and ๐ can take values ( 1 , 2 , 3 ) . The joint distribution of ๐ and ๐ is shown in the table below ๐ 1 2 3 ๐ 4 0.1 0.30 0.20 5 0.1 0.05 0.25 Using this information, please compute the unconditional expected value ๐ธ ( ๐ ) and the conditional expected value ๐ธ ( ๐ | ๐ = 2 ) . (Please round your results to the 4th decimal place.)
Options
A.๐ธ
(
๐
)
=
2.25
;
๐ธ
(
๐
|
๐
=
2
)
=
4.1429
B.๐ธ
(
๐
)
=
4.5
;
๐ธ
(
๐
|
๐
=
2
)
=
4.5
C.๐ธ
(
๐
)
=
4.4
;
๐ธ
(
๐
|
๐
=
2
)
=
4.1429
D.๐ธ
(
๐
)
=
4.4
;
๐ธ
(
๐
|
๐
=
2
)
=
4.5
E.๐ธ
(
๐
)
=
2.25
;
๐ธ
(
๐
|
๐
=
2
)
=
2.375
F.๐ธ
(
๐
)
=
4.4
;
๐ธ
(
๐
|
๐
=
2
)
=
2.375
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Step-by-Step Analysis
We begin by restating the problem and listing the options to be evaluated.
Question: Given X โ {4,5} and Y โ {1,2,3} with the joint distribution shown, compute the unconditional E(X) and the conditional E(X | Y=2), rounding to 4 decimals.
Options to analyze:
1) E(X)=2.25; E(X|Y=2)=4.1429
2) E(X)=4.5; E(X|Y=2)=4.5
3) E(X)=4.4; E(X|Y=2)=4.1429
4) E(X)=4.4; E(X|Y=2)=4.5
5) E(X)=2.25; E(X|Y=2)=2.375
6) E(X)=4.4; E(X|Y=2)=2.375
First, compute the uncon......Login to view full explanationLog in for full answers
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