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2. The function given by y = f(x) y = f (x) is, itself, named and denoted as f: x ↦ y f: x ↦ y which, for all intents and purposes, could just as well be stated as an equality f = (x ↦ y) f = (x ↦ y), though people don't generally use the notation that way, as well. An alternate - and more standard - notation for denoting a function ...
Something that has been really confusing me lately is that this equation has four solutions $$3x(x+1)(x^2+x+2)=16x(x+1)(2x+1)$$ But what does that mean? Until now solutions to me has meant, what a...
$\begingroup$ Funny thing is that given the density of Gaussian you do not need even an integration to find the mean and variance! $\endgroup$ – Arash Commented Oct 8, 2013 at 0:40
$\begingroup$ @Brian M. Scott What does it mean when each subscript is non-numerical, and is exactly the same? I have an equation that has a value T (temperature in Kelvin), subscripted gamma. It's used several times each the same way, no variation, and all other equations in the same family simply use T, unsubscripted. What might that mean ...
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Summing all products gives us the total sum of all values, and dividing it by the number of observations yields the mean. On the other hand, to calculate the median from a histogram you have to apply the following classical formula: Lm +[N 2 −Fm−1 fm] ⋅ c L m + [N 2 − F m − 1 f m] ⋅ c. where Lm L m is the lower limit of the median ...
I was asked to derive the mean and variance for the negative binomial using the moment generating function of the negative binomial. However i am not sure how to go about using the formula to go out and actually solve for the mean and variance.
No, $\mathbb{R}^2$ means the space of $2$ dimensional vectors. For example $$ \pmatrix{7 \\ -2} $$ is an example of an element in $\mathbb{R}^2$.
Writing {\displaystyle x\in A} x\in A means that "x is an element of A". Equivalent expressions are "x is a member of A", "x belongs to A", "x is in A" and "x lies in A". The expressions "A includes x" and "A contains x" are also used to mean set membership, however some authors use them to mean instead "x is a subset of A".
You can calculate (or look up) how many standard deviations away from the mean you are at 4%. Given this, you multiply the number of standard deviations from the mean by the standard deviation (in lbs) to see how many lbs away from the mean you are. You know one end (20 lbs) and you can now find the other end, which is the mean.