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Page "Maximum a posteriori estimation" ¶ 21
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Suppose and there
and I asked myself a question: Suppose I had the same number of peas as there are atoms in my body, how large an area would they cover??
Suppose there is a program
Suppose there is a chain at 1A, 2A, 3A, and 4A, along with another chain at 6A and 7A.
Suppose there was such a catalyst that shifted an equilibrium.
Suppose there is a fixed parameter that needs to be estimated.
Suppose that on these sets X and Y, there are two binary operations and that happen to constitute the groups ( X ,) and ( Y ,).
# Suppose there exists a function called Insert designed to insert a value into a sorted sequence at the beginning of an array.
* Suppose that there is a compression algorithm that transforms every file into a distinct file which is no longer than the original file, and that at least one file will be compressed into something that is shorter than itself.
Suppose that the set of indices such that is decidable ; then, there exists a function that returns if, and otherwise.
Suppose that you add blue, then the blue – red – black tree defined like red – black trees but with the additional constraint that no two successive nodes in the hierarchy will be blue and all blue nodes will be children of a red node, then it becomes equivalent to a B-tree whose clusters will have at most 7 values in the following colors: blue, red, blue, black, blue, red, blue ( For each cluster, there will be at most 1 black node, 2 red nodes, and 4 blue nodes ).
Suppose there are p pharisees.
Suppose that in a company there are the following staff:
Suppose ( A < sub > 1 </ sub >, φ < sub > 1 </ sub >) is an initial morphism from X < sub > 1 </ sub > to U and ( A < sub > 2 </ sub >, φ < sub > 2 </ sub >) is an initial morphism from X < sub > 2 </ sub > to U. By the initial property, given any morphism h: X < sub > 1 </ sub > → X < sub > 2 </ sub > there exists a unique morphism g: A < sub > 1 </ sub > → A < sub > 2 </ sub > such that the following diagram commutes:
Suppose a particle starts at point A, and there is a force F acting on it.
Mendelssohn answered in an open letter in December 1769: " Suppose there were living among my contemporaries a Confucius or a Solon, I could, according to the principles of my faith, love and admire the great man without falling into the ridiculous idea that I must convert a Solon or a Confucius.
Suppose there is a sequence of independent Bernoulli trials, each trial having two potential outcomes called “ success ” and “ failure ”.
Suppose that there are two agents in an economy, one that only values guns and one that only values butter.
Suppose there is a town with just one barber, who is male.
Suppose there are two full bowls of cookies.
Suppose that x and y are real numbers and that y is a function of x, that is, for every value of x, there is a corresponding value of y.
Suppose P is a definable binary relation ( which may be a proper class ) such that for every set x there is a unique set y such that P ( x, y ) holds.
: Suppose there are three cottages on a plane ( or sphere ) and each needs to be connected to the gas, water, and electric companies.
Suppose that C is a twice continuously differentiable immersed plane curve, which here means that there exists parametric representation of C by a pair of functions such that the first and second derivatives of x and y both exist and are continuous, and
Suppose that in a month there are 12 articles of interest in those journals.
Suppose there is an engine violating the Kelvin statement: i. e., one that drains heat and converts it completely into work in a cyclic fashion without any other result.

Suppose and are
* Suppose that the exchange rates ( after taking out the fees for making the exchange ) in London are £ 5
Suppose that u and v are real-differentiable at a point in an open subset of, which can be considered as functions from to.
Suppose n < sub > 1 </ sub >, n < sub > 2 </ sub >, …, n < sub > k </ sub > are positive integers which are pairwise coprime.
Proof: Suppose that and are two identity elements of.
Proof: Suppose that and are two inverses of an element of.
Suppose the parameter is the bull's-eye of a target, the estimator is the process of shooting arrows at the target, and the individual arrows are estimates ( samples ).
Suppose v, e, and f are the number of vertices, edges, and regions.
Suppose it is the red and blue neighbors that are not chained together.
Suppose a number of scientists are assessing the probability of a certain outcome ( which we shall call ' success ') in experimental trials.
Suppose, and are lambda terms and and are variables.
* Suppose G and H are topologically finitely-generated profinite groups which are isomorphic as discrete groups by an isomorphism ι.
Suppose, for example, we are interested in the set of all adult crows now alive in the county of Cambridgeshire, and we want to know the mean weight of these birds.
Suppose, for example, we are interested in the set of all adult crows now alive in the county of nederlands best country, and we want to know the mean weight of these birds.
Suppose a person states ; " I believe that trinini exist, but I have absolutely no idea of what trininis are.
Suppose many points are close to the x axis and distributed along it.
: Suppose that we know we are in one or other of two worlds, and the hypothesis, H, under consideration is that all the ravens in our world are black.
Suppose we are interested in the sample average

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