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95. if the coefficient of correlation between × and y is 0.5, the covariance is and if the standard deviation of x is 4 then Standard deviation of y is.
(a) 4
0 • 5
Cov (y 4) = 16
(b)
8*
64 L
(c) 16
(d) 64?
(a) 4
0 • 5
Cov (y 4) = 16
(b)
8*
64 L
(c) 16
(d) 64?
Most Upvoted Answer
95. if the coefficient of correlation between × and y is 0.5, the cova...
Understanding Correlation and Covariance
To determine the standard deviation of \( y \) given the correlation coefficient and standard deviation of \( x \), we can use the formula that relates these variables.
Given Data
- Coefficient of correlation (\( r \)) = 0.5
- Standard deviation of \( x \) (\( \sigma_x \)) = 4
Formula for Covariance
The covariance between \( x \) and \( y \) can be calculated using the formula:
\[
Cov(x, y) = r \cdot \sigma_x \cdot \sigma_y
\]
Where:
- \( Cov(x, y) \) = Covariance between \( x \) and \( y \)
- \( r \) = Coefficient of correlation
- \( \sigma_x \) = Standard deviation of \( x \)
- \( \sigma_y \) = Standard deviation of \( y \)
Calculating Standard Deviation of \( y \)
From the formula, we can rearrange it to find \( \sigma_y \):
\[
\sigma_y = \frac{Cov(x, y)}{r \cdot \sigma_x}
\]
However, we don't have the covariance directly. But if we assume \( Cov(x, y) = 16 \) (as per the options), we can substitute the values into the equation:
\[
\sigma_y = \frac{16}{0.5 \cdot 4}
\]
Calculating this gives:
\[
\sigma_y = \frac{16}{2} = 8
\]
Conclusion
Thus, the standard deviation of \( y \) is:
- \( \sigma_y = 8 \)
Based on the options provided, the answer corresponds to:
- (b) 8
Therefore, the solution is confirmed that the standard deviation of \( y \) is indeed \( 8 \).
To determine the standard deviation of \( y \) given the correlation coefficient and standard deviation of \( x \), we can use the formula that relates these variables.
Given Data
- Coefficient of correlation (\( r \)) = 0.5
- Standard deviation of \( x \) (\( \sigma_x \)) = 4
Formula for Covariance
The covariance between \( x \) and \( y \) can be calculated using the formula:
\[
Cov(x, y) = r \cdot \sigma_x \cdot \sigma_y
\]
Where:
- \( Cov(x, y) \) = Covariance between \( x \) and \( y \)
- \( r \) = Coefficient of correlation
- \( \sigma_x \) = Standard deviation of \( x \)
- \( \sigma_y \) = Standard deviation of \( y \)
Calculating Standard Deviation of \( y \)
From the formula, we can rearrange it to find \( \sigma_y \):
\[
\sigma_y = \frac{Cov(x, y)}{r \cdot \sigma_x}
\]
However, we don't have the covariance directly. But if we assume \( Cov(x, y) = 16 \) (as per the options), we can substitute the values into the equation:
\[
\sigma_y = \frac{16}{0.5 \cdot 4}
\]
Calculating this gives:
\[
\sigma_y = \frac{16}{2} = 8
\]
Conclusion
Thus, the standard deviation of \( y \) is:
- \( \sigma_y = 8 \)
Based on the options provided, the answer corresponds to:
- (b) 8
Therefore, the solution is confirmed that the standard deviation of \( y \) is indeed \( 8 \).
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95. if the coefficient of correlation between × and y is 0.5, the covariance is and if the standard deviation of x is 4 then Standard deviation of y is.(a) 40 • 5Cov (y 4) = 16(b)8*64 L(c) 16(d) 64?
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95. if the coefficient of correlation between × and y is 0.5, the covariance is and if the standard deviation of x is 4 then Standard deviation of y is.(a) 40 • 5Cov (y 4) = 16(b)8*64 L(c) 16(d) 64? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 95. if the coefficient of correlation between × and y is 0.5, the covariance is and if the standard deviation of x is 4 then Standard deviation of y is.(a) 40 • 5Cov (y 4) = 16(b)8*64 L(c) 16(d) 64? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 95. if the coefficient of correlation between × and y is 0.5, the covariance is and if the standard deviation of x is 4 then Standard deviation of y is.(a) 40 • 5Cov (y 4) = 16(b)8*64 L(c) 16(d) 64?.
95. if the coefficient of correlation between × and y is 0.5, the covariance is and if the standard deviation of x is 4 then Standard deviation of y is.(a) 40 • 5Cov (y 4) = 16(b)8*64 L(c) 16(d) 64? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 95. if the coefficient of correlation between × and y is 0.5, the covariance is and if the standard deviation of x is 4 then Standard deviation of y is.(a) 40 • 5Cov (y 4) = 16(b)8*64 L(c) 16(d) 64? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 95. if the coefficient of correlation between × and y is 0.5, the covariance is and if the standard deviation of x is 4 then Standard deviation of y is.(a) 40 • 5Cov (y 4) = 16(b)8*64 L(c) 16(d) 64?.
Solutions for 95. if the coefficient of correlation between × and y is 0.5, the covariance is and if the standard deviation of x is 4 then Standard deviation of y is.(a) 40 • 5Cov (y 4) = 16(b)8*64 L(c) 16(d) 64? in English & in Hindi are available as part of our courses for UPSC.
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