GATE Exam > GATE Questions > Let (X1 , X2) be independent random variables...
Start Learning for Free
Let (X1 , X2) be independent random variables. X1 has mean 0 and variance 1, while X2 has mean 1 and variance 4. The mutual information I (X1; X2) between X1 and X2 in bits is _________.
Correct answer is between '0.0,0.0'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Let (X1 , X2) be independent random variables. X1 has mean 0 and varia...
For two independent random variable
I(X;Y) = H(X) = H(X/Y)
H(X/Y) = H(X) or independent X and Y
⇒I(X;Y) = 0
I(X;Y) = H(X) = H(X/Y)
H(X/Y) = H(X) or independent X and Y
⇒I(X;Y) = 0
Most Upvoted Answer
Let (X1 , X2) be independent random variables. X1 has mean 0 and varia...
Solution:
Mutual Information (MI) is a measure of the amount of information that two random variables share.
MI(X1,X2) = H(X1) - H(X1|X2)
where H(X1) is the entropy of X1 and H(X1|X2) is the conditional entropy of X1 given X2.
Calculating H(X1):
Since X1 has a mean of 0 and variance of 1, we can assume that X1 follows a standard normal distribution.
H(X1) = 0.5*log(2*pi*e*1^2) = 0.5*log(2*pi*e)
Calculating H(X1|X2):
Since X1 and X2 are independent, H(X1|X2) = H(X1).
Therefore,
MI(X1,X2) = H(X1) - H(X1|X2) = 0.5*log(2*pi*e) - 0.5*log(2*pi*e) = 0.
Hence, the mutual information between X1 and X2 is 0 bits.
Mutual Information (MI) is a measure of the amount of information that two random variables share.
MI(X1,X2) = H(X1) - H(X1|X2)
where H(X1) is the entropy of X1 and H(X1|X2) is the conditional entropy of X1 given X2.
Calculating H(X1):
Since X1 has a mean of 0 and variance of 1, we can assume that X1 follows a standard normal distribution.
H(X1) = 0.5*log(2*pi*e*1^2) = 0.5*log(2*pi*e)
Calculating H(X1|X2):
Since X1 and X2 are independent, H(X1|X2) = H(X1).
Therefore,
MI(X1,X2) = H(X1) - H(X1|X2) = 0.5*log(2*pi*e) - 0.5*log(2*pi*e) = 0.
Hence, the mutual information between X1 and X2 is 0 bits.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
Let (X1 , X2) be independent random variables. X1 has mean 0 and variance 1, while X2 has mean 1 and variance 4. The mutual information I (X1; X2) between X1 and X2 in bits is _________.Correct answer is between '0.0,0.0'. Can you explain this answer?
Question Description
Let (X1 , X2) be independent random variables. X1 has mean 0 and variance 1, while X2 has mean 1 and variance 4. The mutual information I (X1; X2) between X1 and X2 in bits is _________.Correct answer is between '0.0,0.0'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Let (X1 , X2) be independent random variables. X1 has mean 0 and variance 1, while X2 has mean 1 and variance 4. The mutual information I (X1; X2) between X1 and X2 in bits is _________.Correct answer is between '0.0,0.0'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let (X1 , X2) be independent random variables. X1 has mean 0 and variance 1, while X2 has mean 1 and variance 4. The mutual information I (X1; X2) between X1 and X2 in bits is _________.Correct answer is between '0.0,0.0'. Can you explain this answer?.
Let (X1 , X2) be independent random variables. X1 has mean 0 and variance 1, while X2 has mean 1 and variance 4. The mutual information I (X1; X2) between X1 and X2 in bits is _________.Correct answer is between '0.0,0.0'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Let (X1 , X2) be independent random variables. X1 has mean 0 and variance 1, while X2 has mean 1 and variance 4. The mutual information I (X1; X2) between X1 and X2 in bits is _________.Correct answer is between '0.0,0.0'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let (X1 , X2) be independent random variables. X1 has mean 0 and variance 1, while X2 has mean 1 and variance 4. The mutual information I (X1; X2) between X1 and X2 in bits is _________.Correct answer is between '0.0,0.0'. Can you explain this answer?.
Solutions for Let (X1 , X2) be independent random variables. X1 has mean 0 and variance 1, while X2 has mean 1 and variance 4. The mutual information I (X1; X2) between X1 and X2 in bits is _________.Correct answer is between '0.0,0.0'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of Let (X1 , X2) be independent random variables. X1 has mean 0 and variance 1, while X2 has mean 1 and variance 4. The mutual information I (X1; X2) between X1 and X2 in bits is _________.Correct answer is between '0.0,0.0'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Let (X1 , X2) be independent random variables. X1 has mean 0 and variance 1, while X2 has mean 1 and variance 4. The mutual information I (X1; X2) between X1 and X2 in bits is _________.Correct answer is between '0.0,0.0'. Can you explain this answer?, a detailed solution for Let (X1 , X2) be independent random variables. X1 has mean 0 and variance 1, while X2 has mean 1 and variance 4. The mutual information I (X1; X2) between X1 and X2 in bits is _________.Correct answer is between '0.0,0.0'. Can you explain this answer? has been provided alongside types of Let (X1 , X2) be independent random variables. X1 has mean 0 and variance 1, while X2 has mean 1 and variance 4. The mutual information I (X1; X2) between X1 and X2 in bits is _________.Correct answer is between '0.0,0.0'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let (X1 , X2) be independent random variables. X1 has mean 0 and variance 1, while X2 has mean 1 and variance 4. The mutual information I (X1; X2) between X1 and X2 in bits is _________.Correct answer is between '0.0,0.0'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup