Suppose that a speaker can have the concept of water we do only if the speaker lives in a world that contains H < sub > 2 </ sub > O.

Suppose a is thrown that contains six sides and that the numeric result of the throw corresponds to a quantum mechanics observable.

: Suppose X is a compact Hausdorff space and A is a subalgebra of C ( X, R ) which contains a non-zero constant function.

As they discussed Shelvocke's book, Wordsworth proffers the following developmental critique to Coleridge, which importantly contains a reference to tutelary spirits: " Suppose you represent him as having killed one of these birds on entering the south sea, and the tutelary spirits of these regions take upon them to avenge the crime.

Suppose that a country ( or other entity ) contains Population < sub > t </ sub > persons at time t.

Suppose a partially ordered set P has the property that every chain ( i. e. totally ordered subset ) has an upper bound in P. Then the set P contains at least one maximal element.

Suppose a non-empty partially ordered set P has the property that every non-empty chain has an upper bound in P. Then the set P contains at least one maximal element.

Suppose G is an ordered abelian group, meaning an abelian group with a total ordering "<" respecting the group's addition, so that a < b if and only if a + c < b + c for all c. Let I be a well-ordered subset of G, meaning I contains no infinite descending chain.

Suppose each level contains

Suppose we want to define an extremely simple XML markup scheme for a book: a book is defined as a sequence of one or more pages ; each page contains text only.

Suppose also, M contains the identity operator on H.

Suppose that a 2-satisfiability instance contains two clauses that both use the same variable x, but that x is negated in one clause and not in the other.

Suppose that R is an algebra over the field C of complex numbers and M = N is a finite-dimensional simple module over R. Then Schur's lemma says that the endomorphism ring of the module M is a division ring ; this division ring contains C in its center, is finite-dimensional over C and is therefore equal to C. Thus the endomorphism ring of the module M is " as small as possible ".

Suppose an experimenter performs 10 measurements all at exactly the same value of independent variable vector X ( which contains the independent variables X < sub > 1 </ sub >, X < sub > 2 </ sub >, and X < sub > 3 </ sub >).

Suppose a program contains several classes in an inheritance hierarchy: a superclass,, and two subclasses, and.

Suppose you have a collection of lists, each node of a list contains an object, the name of the list to which it belongs, and the number of elements in that list.

Suppose that the Fuchsian group G contains a parabolic element g. For example, the element t ∈ SL ( 2, Z ) where

Suppose a data store contains N data objects, and it is desired to retrieve one of them based on the value of one of the object's fields.

Suppose the file " foo. xml " contains this XML document:

Suppose the seed line A contains an allele a, and a seed line B of the same crop species contains an allele b, for the same gene.

Suppose that Y is the sum of n identically distributed independent random variables all with the same distribution as X.

Suppose there is a sequence of independent Bernoulli trials, each trial having two potential outcomes called “ success ” and “ failure ”.

Suppose a process is generating independent and identically distributed events, but the probability distribution is unknown.

Suppose that you are popping one hundred kernels of popcorn, and each kernel will pop at an independent, uniformly random time within the next hundred seconds.

Suppose there is a sample of n independent and identically distributed observations, coming from a distribution with an unknown probability density function f < sub > 0 </ sub >(·).

Suppose the feasible set of the SAA problem is fixed, i. e., it is independent of the sample.

Suppose U < sub > 1 </ sub >, ..., U < sub > n </ sub > are independent standard normally distributed random variables, and an identity of the form

Suppose X < sub > 1 </ sub >, ..., X < sub > n </ sub > are independent and identically distributed, and are normally distributed with unknown expected value μ and known variance 1.

Suppose ( unrealistically ) that the number N is chosen by some random process that is independent of the batter's ability – say a coin is tossed after each at-bat and the result determines whether the scout will stay to watch the batter's next at-bat.

Suppose these Xs are conditionally independent given p.

Suppose X and Y are two independent tosses of a fair coin, where we designate 1 for heads and 0 for tails.

Suppose that everywhere on the constrained set, the n derivatives of the n functions are all linearly independent and also that the Poisson brackets

Suppose now that X < sub > 1 </ sub >, ..., X < sub > n </ sub > are independent and identically distributed samples from the distribution above.

Suppose that the products are sold in separate markets ( this is commonly the case ) so demands are independent, and demand for good n is with inverse demand function Total revenue is

Suppose for simplicity that a certain system is characterized by two variables-a dependent variable x and an independent variable t, where x is a function of t. Both x and t represent quantities with units.

To estimate these parameters, a single measurement X < sub > i </ sub > is performed for each parameter θ < sub > i </ sub >, resulting in a vector X of length n. Suppose the measurements are independent, Gaussian random variables, with mean θ and variance 1, i. e.,

Suppose we have independent Gaussian measurements of each of these quantities.

Suppose that we do not get a perfect measure of one of our independent variables.

Suppose that the level of pest infestation is independent of all other factors within a given period, but is influenced by the level of rainfall and fertilizer in the preceding period.

Suppose further that for any n elements x < sub > 1 </ sub >,..., x < sub > n </ sub > of F which are linearly independent over Q, the extension field Q ( x < sub > 1 </ sub >,..., x < sub > n </ sub >, e ( x < sub > 1 </ sub >),..., e ( x < sub > n </ sub >)) has transcendence degree at least n over Q.

Suppose X < sub > 1 </ sub >, ..., X < sub > n </ sub > are independent identically distributed random variables with a gamma distribution with probability density function

Suppose independent observations are made for three populations,, and.