CA Foundation Exam > CA Foundation Questions > If the covariance between two variables is 20...
Start Learning for Free
If the covariance between two variables is 20 and the variance of one of the variables is 16, what would be the variance of the other variable?
- a)More than 100
- b)More than 10
- c)Less than 10
- d)More than 1.25
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
If the covariance between two variables is 20 and the variance of one ...
Solution:
Given, Covariance between two variables = 20
Variance of one of the variables = 16
Let the two variables be X and Y.
Covariance formula is given as:
Cov(X, Y) = E[(X - μX)(Y - μY)]
where E is the expected value, μX and μY are the means of X and Y respectively.
We can rewrite the covariance formula as:
Cov(X, Y) = E[XY] - μXμY
Now, we can use this formula to find the variance of the other variable.
Variance formula is given as:
Var(Y) = E[(Y - μY)²]
We can rewrite the variance formula as:
Var(Y) = E[Y²] - μY²
Now, we can use the covariance formula and the variance formula to find Var(Y).
Var(Y) = Cov(X, Y) + μXμY (from covariance formula)
We know that Cov(X, Y) = 20 and Var(X) = 16.
Let us assume that μX = μY = μ (for simplicity).
Then, we can write:
Var(X) = E[X²] - μ² (from variance formula)
16 = E[X²] - μ²
E[X²] = 16 + μ²
Similarly, we can write:
Cov(X, Y) = E[XY] - μ² (from covariance formula)
20 = E[XY] - μ²
E[XY] = 20 + μ²
Now, we can substitute these values in the expression for Var(Y).
Var(Y) = Cov(X, Y) + μXμY
Var(Y) = 20 + μ² + μ²
Var(Y) = 2μ² + 20
We can see that Var(Y) depends on μ², which can take any positive value.
Therefore, Var(Y) can be more than 100.
Hence, option A is the correct answer.
Given, Covariance between two variables = 20
Variance of one of the variables = 16
Let the two variables be X and Y.
Covariance formula is given as:
Cov(X, Y) = E[(X - μX)(Y - μY)]
where E is the expected value, μX and μY are the means of X and Y respectively.
We can rewrite the covariance formula as:
Cov(X, Y) = E[XY] - μXμY
Now, we can use this formula to find the variance of the other variable.
Variance formula is given as:
Var(Y) = E[(Y - μY)²]
We can rewrite the variance formula as:
Var(Y) = E[Y²] - μY²
Now, we can use the covariance formula and the variance formula to find Var(Y).
Var(Y) = Cov(X, Y) + μXμY (from covariance formula)
We know that Cov(X, Y) = 20 and Var(X) = 16.
Let us assume that μX = μY = μ (for simplicity).
Then, we can write:
Var(X) = E[X²] - μ² (from variance formula)
16 = E[X²] - μ²
E[X²] = 16 + μ²
Similarly, we can write:
Cov(X, Y) = E[XY] - μ² (from covariance formula)
20 = E[XY] - μ²
E[XY] = 20 + μ²
Now, we can substitute these values in the expression for Var(Y).
Var(Y) = Cov(X, Y) + μXμY
Var(Y) = 20 + μ² + μ²
Var(Y) = 2μ² + 20
We can see that Var(Y) depends on μ², which can take any positive value.
Therefore, Var(Y) can be more than 100.
Hence, option A is the correct answer.
Free Test
FREE
| Start Free Test |
Community Answer
If the covariance between two variables is 20 and the variance of one ...
Given, Cov (x, y) =20
and variance of one of the variables is 16.
so the standard deviation SD is 4.
we know the formula,
r= cov (x, y) /(SD of x * SD of Y)
r= 20 /4 * SD of the other variable
r= 5/ SD of the other variable
we also know that coefficient of correlation, r, lies between -1 and +1 including them.
so, SD of the other variable has to be atleast 5 or more.
so the variance will be 5^2 = 25 atleast or more.
i dont know why the icai book says the answer is more than 100. if anybody can match the answer with book then please tell me.
and variance of one of the variables is 16.
so the standard deviation SD is 4.
we know the formula,
r= cov (x, y) /(SD of x * SD of Y)
r= 20 /4 * SD of the other variable
r= 5/ SD of the other variable
we also know that coefficient of correlation, r, lies between -1 and +1 including them.
so, SD of the other variable has to be atleast 5 or more.
so the variance will be 5^2 = 25 atleast or more.
i dont know why the icai book says the answer is more than 100. if anybody can match the answer with book then please tell me.
Attention CA Foundation Students!
To make sure you are not studying endlessly, EduRev has designed CA Foundation study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CA Foundation.
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
If the covariance between two variables is 20 and the variance of one of the variables is 16, what would be the variance of the other variable?a)More than 100b)More than 10c)Less than 10d)More than 1.25Correct answer is option 'A'. Can you explain this answer?
Question Description
If the covariance between two variables is 20 and the variance of one of the variables is 16, what would be the variance of the other variable?a)More than 100b)More than 10c)Less than 10d)More than 1.25Correct answer is option 'A'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the covariance between two variables is 20 and the variance of one of the variables is 16, what would be the variance of the other variable?a)More than 100b)More than 10c)Less than 10d)More than 1.25Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the covariance between two variables is 20 and the variance of one of the variables is 16, what would be the variance of the other variable?a)More than 100b)More than 10c)Less than 10d)More than 1.25Correct answer is option 'A'. Can you explain this answer?.
If the covariance between two variables is 20 and the variance of one of the variables is 16, what would be the variance of the other variable?a)More than 100b)More than 10c)Less than 10d)More than 1.25Correct answer is option 'A'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the covariance between two variables is 20 and the variance of one of the variables is 16, what would be the variance of the other variable?a)More than 100b)More than 10c)Less than 10d)More than 1.25Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the covariance between two variables is 20 and the variance of one of the variables is 16, what would be the variance of the other variable?a)More than 100b)More than 10c)Less than 10d)More than 1.25Correct answer is option 'A'. Can you explain this answer?.
Solutions for If the covariance between two variables is 20 and the variance of one of the variables is 16, what would be the variance of the other variable?a)More than 100b)More than 10c)Less than 10d)More than 1.25Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of If the covariance between two variables is 20 and the variance of one of the variables is 16, what would be the variance of the other variable?a)More than 100b)More than 10c)Less than 10d)More than 1.25Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If the covariance between two variables is 20 and the variance of one of the variables is 16, what would be the variance of the other variable?a)More than 100b)More than 10c)Less than 10d)More than 1.25Correct answer is option 'A'. Can you explain this answer?, a detailed solution for If the covariance between two variables is 20 and the variance of one of the variables is 16, what would be the variance of the other variable?a)More than 100b)More than 10c)Less than 10d)More than 1.25Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of If the covariance between two variables is 20 and the variance of one of the variables is 16, what would be the variance of the other variable?a)More than 100b)More than 10c)Less than 10d)More than 1.25Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If the covariance between two variables is 20 and the variance of one of the variables is 16, what would be the variance of the other variable?a)More than 100b)More than 10c)Less than 10d)More than 1.25Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup