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A voltage V1 is measured 100 times and its average and standard deviation are 100 V and 1.5 V respectively. A second voltage V2, which is independent of V1, is measured 200 times and its average and standard deviation are 150 V and 2 V respectively. V3 is computed as: V3 = V1 + V2.
Then the standard deviation of V3 in volt is ___________.
Correct answer is '2.5'. Can you explain this answer?
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A voltage V1 is measured 100 times and its average and standard deviat...
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A voltage V1 is measured 100 times and its average and standard deviat...
To find the standard deviation of V3, we need to understand how the standard deviations of V1 and V2 affect the standard deviation of V3.
Let's break down the problem step by step:
1. Average and standard deviation of V1:
- Average of V1 = 100 V
- Standard deviation of V1 = 1.5 V
2. Average and standard deviation of V2:
- Average of V2 = 150 V
- Standard deviation of V2 = 2 V
3. Computation of V3:
- V3 = V1 - V2 (since V3 = V1 + (-V2))
- The average of V3 would be the difference of the averages of V1 and V2:
- Average of V3 = Average of V1 - Average of V2 = 100 V - 150 V = -50 V
- To find the standard deviation of V3, we need to consider the variances of V1 and V2 and their covariance. The variance of V3 can be calculated as follows:
- Variance of V3 = Variance of (V1 - V2) = Variance of V1 + Variance of V2 - 2 * Covariance of (V1, V2)
- Covariance of (V1, V2) = 0 (since V1 and V2 are independent)
4. Calculation of standard deviation of V3:
- Standard deviation of V3 = Square root of Variance of V3
- Standard deviation of V3 = Square root of (Variance of V1 + Variance of V2 - 2 * Covariance of (V1, V2))
- Standard deviation of V3 = Square root of (1.5^2 + 2^2 - 2 * 0)
- Standard deviation of V3 = Square root of (2.25 + 4)
- Standard deviation of V3 = Square root of 6.25
- Standard deviation of V3 = 2.5 V
Therefore, the standard deviation of V3 is 2.5 V.
Let's break down the problem step by step:
1. Average and standard deviation of V1:
- Average of V1 = 100 V
- Standard deviation of V1 = 1.5 V
2. Average and standard deviation of V2:
- Average of V2 = 150 V
- Standard deviation of V2 = 2 V
3. Computation of V3:
- V3 = V1 - V2 (since V3 = V1 + (-V2))
- The average of V3 would be the difference of the averages of V1 and V2:
- Average of V3 = Average of V1 - Average of V2 = 100 V - 150 V = -50 V
- To find the standard deviation of V3, we need to consider the variances of V1 and V2 and their covariance. The variance of V3 can be calculated as follows:
- Variance of V3 = Variance of (V1 - V2) = Variance of V1 + Variance of V2 - 2 * Covariance of (V1, V2)
- Covariance of (V1, V2) = 0 (since V1 and V2 are independent)
4. Calculation of standard deviation of V3:
- Standard deviation of V3 = Square root of Variance of V3
- Standard deviation of V3 = Square root of (Variance of V1 + Variance of V2 - 2 * Covariance of (V1, V2))
- Standard deviation of V3 = Square root of (1.5^2 + 2^2 - 2 * 0)
- Standard deviation of V3 = Square root of (2.25 + 4)
- Standard deviation of V3 = Square root of 6.25
- Standard deviation of V3 = 2.5 V
Therefore, the standard deviation of V3 is 2.5 V.
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A voltage V1 is measured 100 times and its average and standard deviation are 100 V and 1.5 Vrespectively. A second voltage V2, which is independent of V1, is measured 200 times and itsaverage and standard deviation are 150 V and 2 V respectively. V3 is computed as: V3 = V1 + V2.Then the standard deviation of V3 in volt is ___________.Correct answer is '2.5'. Can you explain this answer?
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A voltage V1 is measured 100 times and its average and standard deviation are 100 V and 1.5 Vrespectively. A second voltage V2, which is independent of V1, is measured 200 times and itsaverage and standard deviation are 150 V and 2 V respectively. V3 is computed as: V3 = V1 + V2.Then the standard deviation of V3 in volt is ___________.Correct answer is '2.5'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A voltage V1 is measured 100 times and its average and standard deviation are 100 V and 1.5 Vrespectively. A second voltage V2, which is independent of V1, is measured 200 times and itsaverage and standard deviation are 150 V and 2 V respectively. V3 is computed as: V3 = V1 + V2.Then the standard deviation of V3 in volt is ___________.Correct answer is '2.5'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A voltage V1 is measured 100 times and its average and standard deviation are 100 V and 1.5 Vrespectively. A second voltage V2, which is independent of V1, is measured 200 times and itsaverage and standard deviation are 150 V and 2 V respectively. V3 is computed as: V3 = V1 + V2.Then the standard deviation of V3 in volt is ___________.Correct answer is '2.5'. Can you explain this answer?.
A voltage V1 is measured 100 times and its average and standard deviation are 100 V and 1.5 Vrespectively. A second voltage V2, which is independent of V1, is measured 200 times and itsaverage and standard deviation are 150 V and 2 V respectively. V3 is computed as: V3 = V1 + V2.Then the standard deviation of V3 in volt is ___________.Correct answer is '2.5'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A voltage V1 is measured 100 times and its average and standard deviation are 100 V and 1.5 Vrespectively. A second voltage V2, which is independent of V1, is measured 200 times and itsaverage and standard deviation are 150 V and 2 V respectively. V3 is computed as: V3 = V1 + V2.Then the standard deviation of V3 in volt is ___________.Correct answer is '2.5'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A voltage V1 is measured 100 times and its average and standard deviation are 100 V and 1.5 Vrespectively. A second voltage V2, which is independent of V1, is measured 200 times and itsaverage and standard deviation are 150 V and 2 V respectively. V3 is computed as: V3 = V1 + V2.Then the standard deviation of V3 in volt is ___________.Correct answer is '2.5'. Can you explain this answer?.
Solutions for A voltage V1 is measured 100 times and its average and standard deviation are 100 V and 1.5 Vrespectively. A second voltage V2, which is independent of V1, is measured 200 times and itsaverage and standard deviation are 150 V and 2 V respectively. V3 is computed as: V3 = V1 + V2.Then the standard deviation of V3 in volt is ___________.Correct answer is '2.5'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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