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Numerical Series Expansion
Mathematicians, scientists, and engineers often need solutions for difficult to unsolvable equations in order to progress in their work. Fortunately, through various methods of numerical and polynomial series expansions, some of the most problematic equations can be approximated to easily workable forms. Please post all questions regarding the various expansions and series, such as the Taylor and Maclaurin series expansions, the binomial expansion, and the geometric expansion, as well as the rules that govern them, into this category.
274 Questions
How do you obtain moment generating function Log-normal distribution?
You cannot because it does not exist.
Although all the moments of the lognormal distribution do exist, the distribution is not uniquely determined by its moments. One of the consequences of this is that the expected values E[e^tX] does not converge for any positive t.
What is the next number in the sequence 6-7-10-16-25?
The numbers are increasing in line with the 3 times (multiplication) table.
6-7 is plus 1.
7-10 is plus 3.
10-16 is plus 6.
16-25 is plus 9.
Next in the 3 times table is 12. So, the next number will be 25 + 12.
The answer is 37.
How do you find the maximum number of intersections between a given number of lines?
Use the formula (n2 - n)/2 where n is the given number of lines.
That gives:
(12 - 1)/2 = 0 for one line,
(22 - 2)/2 = 1 for two lines,
(32 - 3)/2 = 3 for three lines,
(42 - 4)/2 = 6 for four lines,
(52 - 5)/2 = 10 for five lines,
and so on.
Add together the values for July, August and September for whatever variable you are studying.
What is The expansion of a binomial that involves a coefficient found by combinations?
Binomial Theorum
When to use poisson distribution?
A Poisson distribution is appropriate when you have events that occur
- independently of one another in space or time,
- at a constant rate, and
- occur singly.
The last condition means that the probability of more than one event occurring at any particular point in space or time is zero (or negligible).
However, if the parameter (mean) of the Poisson distribution, L, is greater than 10, you may be better off using the Normal approximation, N(L, L), with the appropriate continuity corrections.
When things expand, it can block certain things out like a machine
The binomial theorem describes the algebraic expansion of powers of a binomial: that is, the expansion of an expression of the form (x + y)^n where x and y are variables and n is the power to which the binomial is raised. When first encountered, n is a positive integer, but the binomial theorem can be extended to cover values of n which are fractional or negative (or both).
What is the expansion of abbreviation SAT?
The expansion used to be SAT: Scholastic Apptitude Test. Then it got changed to Scholastic Achievement Test. Once it was figured out that the SAT measures not apptitude nor achievement, the SAT doesn't stand for anything now. Interesting enough, look at SAT when it is written by the ETS and there aren't periods after each letter (like they used to be), which indicates that SAT is no longer an abbreviation.
A Laurent's series is a way of representing a complex function as a power series, where a Taylor series expansion is not possible.
The Laurent series for f(z) about a point c, is of the form:
f(z) = sum a(n)*(z - c)^n where the summation is over all integer n: from negative infinity to positive infinity.
The a(n) are constants which are line integrals of f(z). In view of the limitations of this browser: the fact that mathematical symbols are impossible, it is not possible to describe these line integrals.
