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If variance of random variable x is 23, then what is the variance of 2x+10 ?
- a)56
- b)33
- c)46
- d)92
Correct answer is 'D'. Can you explain this answer?
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Verified Answer
If variance of random variable x is 23, then what is the variance of 2...
Uppose X is random variable with mean 'm' and variance 'v'. How does Y=aX+b look like? Let's consider the effect of scaling i.e. multiplication by 'a'. As is very obvious, the scaling just magnifies the data. When you are calculating the variance, you actually sum over the square of difference between a data points and the mean. So, you may see that multiplying by a factor 'a' will result into scaling the variance by a2a2.If you look at the effect of adding 'b' i.e. shifting the whole data. You may notice that that has no effect at the variance because the variance tells us about the scattered-ness of the data about mean. So, when you shift the whole data, you are shifting the mean as well. So, the degree of dispersion is unchanged.In nutshell, V(aX+b) =a2V(X)a2V(X).And using this, one may easily see that V(2X+10)=4V(X)=92V(2X+10)=4V(X)=92.
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Most Upvoted Answer
If variance of random variable x is 23, then what is the variance of 2...
Calculation of Variance of 2x+10:
Given:
Variance of random variable x = 23
Formula for Variance:
Variance of a constant multiplied by a random variable: Var(aX) = a^2 * Var(X)
Calculation:
1. Variance of 2x+10:
Var(2x+10) = Var(2x) = 2^2 * Var(x) = 4 * 23 = 92
Therefore, the variance of 2x+10 is 92.
Conclusion:
The correct option is 'D' - 92.
Given:
Variance of random variable x = 23
Formula for Variance:
Variance of a constant multiplied by a random variable: Var(aX) = a^2 * Var(X)
Calculation:
1. Variance of 2x+10:
Var(2x+10) = Var(2x) = 2^2 * Var(x) = 4 * 23 = 92
Therefore, the variance of 2x+10 is 92.
Conclusion:
The correct option is 'D' - 92.
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If variance of random variable x is 23, then what is the variance of 2x+10 ?a)56b)33c)46d)92Correct answer is 'D'. Can you explain this answer?
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