Two batteries, with voltages V1 and V2, are connected in series. The total voltage V is given by V = V1 + V2. Assume that V1 has mean 12 V and standard deviation 1 V, and that V2 has mean 6 V and standard deviation 0.5 V. Find μV. Assuming V1 and V2 to be independent, find σV.

Given information- We have given data of two batteries which are connected in series. For 1st…

Answered: Two batteries, with voltages V1 and V2,…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.6: Variation

Problem 2E

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Two batteries, with voltages V₁ and V₂, are connected in series. The total voltage V is given by V = V₁ + V₂. Assume that V₁ has mean 12 V and standard deviation 1 V, and that V₂ has mean 6 V and standard deviation 0.5 V. Find μ_V. Assuming V₁ and V₂ to be independent, find σ_V.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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