Another way to compute the mean X ~ Geom(p)) Since ka= Sigma k, j=1, a for any quantity a, we can start the computation of the mean of X ~ Geom(p) as follows: (formula shown in picture below). Now switch the orde
Another way to compute the mean X ~ Geom(p)) Since ka= Sigma k, j=1, a for any quantity a, we can start the computation of the mean of X ~ Geom(p) as follows: (formula shown in picture below). Now switch the orde
Another way to compute the mean X ~ Geom(p)) Since ka= Sigma k, j=1, a for any quantity a, we can start the computation of the mean of X ~ Geom(p) as follows: (formula shown in picture below). Now switch the orde
(Another way to compute the mean X ~ Geom(p)) Since ka= Sigma k, j=1, a for any quantity a, we can start the computation of the mean of X ~ Geom(p) as follows: (formula shown in picture below).
Now switch the order of summation. This means that you take the j-summation outside and put the k-summation inside. But be careful with the limits of the sums. After this you get to the answer by elevating two geometric series.
Transcribed Image Text:Geom(p)) Since
Exercise 3.51. (Another way to compute the mean of X
ka = E-, a for any quantity a, we can start the computation of the mean of
X ~ Geom(p) as follows:
%3D
o k
E(X) = k(1 – p)k-'p = >(1 - p)k=1p.
%3D
k=1
k=1 j=1
Now switch the order of summation. This means that you take the j-summation
outside and put the k-summation inside. But be careful with the limits of the
sums. After this you get to the answer by evaluating two geometric series.
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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