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If the correlation coefficient between X and Y is 0.8 and covariance is 121 and the variance of Y is 64, then variance of X will be
- a)357.59
- b)1237
- c)158
- d)18.91
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If the correlation coefficient between X and Y is 0.8 and covariance i...
Explanation:
Given:
Correlation coefficient (r) = 0.8
Covariance (cov) = 121
Variance of Y (var(Y)) = 64
Formula:
cov(X,Y) = r * σ(X) * σ(Y)
var(Y) = σ(Y)^2
Calculations:
1. Calculate σ(Y)^2:
σ(Y)^2 = 64
2. Calculate σ(X):
121 = 0.8 * σ(X) * √64
121 = 0.8 * σ(X) * 8
σ(X) = 121 / (0.8 * 8) = 121 / 6.4 ≈ 18.91
3. Calculate variance of X (σ(X)^2):
σ(X)^2 = (18.91)^2 ≈ 357.59
Therefore, the variance of X is approximately 357.59, which corresponds to option 'A'.
Given:
Correlation coefficient (r) = 0.8
Covariance (cov) = 121
Variance of Y (var(Y)) = 64
Formula:
cov(X,Y) = r * σ(X) * σ(Y)
var(Y) = σ(Y)^2
Calculations:
1. Calculate σ(Y)^2:
σ(Y)^2 = 64
2. Calculate σ(X):
121 = 0.8 * σ(X) * √64
121 = 0.8 * σ(X) * 8
σ(X) = 121 / (0.8 * 8) = 121 / 6.4 ≈ 18.91
3. Calculate variance of X (σ(X)^2):
σ(X)^2 = (18.91)^2 ≈ 357.59
Therefore, the variance of X is approximately 357.59, which corresponds to option 'A'.
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Community Answer
If the correlation coefficient between X and Y is 0.8 and covariance i...
Concept:
Some useful formulas are:
The correlation coefficient,
σx = √var X
Some useful formulas are:
The correlation coefficient,
σx = √var X
Calculation:
Given, r = 0.8
Cov (X, Y) = 121
Var Y = 64
since Var X = 64, then σy = √64 = 8
∴ σx = 18.91
∴ √var X = 18.91
∴ var X = 357.59
Given, r = 0.8
Cov (X, Y) = 121
Var Y = 64
since Var X = 64, then σy = √64 = 8∴ σx = 18.91
∴ √var X = 18.91
∴ var X = 357.59
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If the correlation coefficient between X and Y is 0.8 and covariance is 121 and the variance of Y is 64, then variance of X will bea)357.59b)1237c)158d)18.91Correct answer is option 'A'. Can you explain this answer?
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