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For a given data, the variance is 15. If each observation is multiplied by 2, what is the new variance of the resulting observations?
- a)15
- b)60
- c)30
- d)7.5
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
For a given data, the variance is 15. If each observation is multiplie...
Variance = 15
New variance = 22*15
= 4*15
= 60
New variance = 22*15
= 4*15
= 60
Most Upvoted Answer
For a given data, the variance is 15. If each observation is multiplie...
Solution:
Given, variance = 15
Let X be the random variable and x1, x2, ..., xn be the observations.
We know that variance of X = Var(X) = E[(X - μ)^2], where μ is the mean of X.
Let Y be the random variable obtained after multiplying each observation of X by 2. Then, Y = 2X.
Mean of Y = E[Y] = E[2X] = 2E[X] = 2μ (using linearity of expectation).
Variance of Y = Var(Y) = E[(Y - 2μ)^2]
= E[(2X - 2μ)^2]
= E[4(X - μ)^2] (using (a-b)^2 = a^2 - 2ab + b^2)
= 4E[(X - μ)^2]
= 4Var(X) (using Var(X) = E[(X - μ)^2])
= 4(15)
= 60
Therefore, the new variance of the resulting observations is 60. Hence, option (b) is correct.
Given, variance = 15
Let X be the random variable and x1, x2, ..., xn be the observations.
We know that variance of X = Var(X) = E[(X - μ)^2], where μ is the mean of X.
Let Y be the random variable obtained after multiplying each observation of X by 2. Then, Y = 2X.
Mean of Y = E[Y] = E[2X] = 2E[X] = 2μ (using linearity of expectation).
Variance of Y = Var(Y) = E[(Y - 2μ)^2]
= E[(2X - 2μ)^2]
= E[4(X - μ)^2] (using (a-b)^2 = a^2 - 2ab + b^2)
= 4E[(X - μ)^2]
= 4Var(X) (using Var(X) = E[(X - μ)^2])
= 4(15)
= 60
Therefore, the new variance of the resulting observations is 60. Hence, option (b) is correct.
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Community Answer
For a given data, the variance is 15. If each observation is multiplie...
Old variance= 15new variance= 2^2*15 =4*
15 =60and
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For a given data, the variance is 15. If each observation is multiplied by 2, what is the new variance of the resulting observations?a)15b)60c)30d)7.5Correct answer is option 'B'. Can you explain this answer?
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