A vector x = (x1 x2) T is jointly Gaussian with zero mean vector and co- matrix variance: Kx = Another vector y = (y1 y2) T is constructed according to y1 = x1 − x2 and y2 = x1 + x2. It is requested: a)Determine the mean vector of y.Determinar a matriz covariância de y. b)Determine whether the y components are independent. c)If the variable x2 is used to replace (predict) the value of x1, what will be the value root mean square of the error committed? And what will be the average value of this error?
A vector x = (x1 x2) T is jointly Gaussian with zero mean vector and co- matrix variance: Kx = Another vector y = (y1 y2) T is constructed according to y1 = x1 − x2 and y2 = x1 + x2. It is requested: a)Determine the mean vector of y.Determinar a matriz covariância de y. b)Determine whether the y components are independent. c)If the variable x2 is used to replace (predict) the value of x1, what will be the value root mean square of the error committed? And what will be the average value of this error?
A vector x = (x1 x2) T is jointly Gaussian with zero mean vector and co- matrix variance: Kx = Another vector y = (y1 y2) T is constructed according to y1 = x1 − x2 and y2 = x1 + x2. It is requested: a)Determine the mean vector of y.Determinar a matriz covariância de y. b)Determine whether the y components are independent. c)If the variable x2 is used to replace (predict) the value of x1, what will be the value root mean square of the error committed? And what will be the average value of this error?
A vector x = (x1 x2) T is jointly Gaussian with zero mean vector and co- matrix variance: Kx = Another vector y = (y1 y2) T is constructed according to y1 = x1 − x2 and y2 = x1 + x2. It is requested: a)Determine the mean vector of y.Determinar a matriz covariância de y. b)Determine whether the y components are independent. c)If the variable x2 is used to replace (predict) the value of x1, what will be the value root mean square of the error committed? And what will be the average value of this error?
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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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