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Suppose Alice and Bob wish to communicate.
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Suppose and Alice
Suppose that Alice and Bob had decided to measure spin along the x-axis.
Suppose Alice has a qubit in some arbitrary quantum state.
Suppose Alice has a qubit that she wants to teleport to Bob.
Suppose Alice wishes to communicate with Bob.
An example: Suppose that only Alice, Bob, and Carol have the keys to a bank safe and that, one day, the contents of the safe are missing ( without the lock being violated ).
Suppose Alice is playing limit Texas hold ' em and is dealt 9 ♣ 9 ♠ under the gun before the flop.
Suppose Alice and Bob want to resolve some dilemma via coin flipping.
Suppose Alice and Bob wish to communicate securely — they may choose to use cryptography.
Suppose Alice wants to prove her identity to Bob.
Suppose Bob wishes to send a message m to Alice whose public key is:
Suppose that the number of puzzles sent by Bob is m, and it takes both Bob and Alice n steps of computation to solve one puzzle.
Suppose Alice and Bob have to decide whether to go to the cinema to see a ' chick flick ', and that each has the liberty to decide whether to go themselves.
Suppose Bob and Alice start with a document containing the word Mary.
Suppose Bob wishes to send a message m to Alice:
Suppose and Bob
Suppose then that Bob bids $ 2. 00 for the item.
Suppose that Bob bids again, this time at $ 2. 75.
Suppose Bob bids one more time, at $ 10. 00.
Suppose that Bob wants to buy a house a year from now.
Suppose Bob likes only chocolate, and Carol only vanilla.
Suppose and wish
Suppose we wish to make it display the next available buffer.
Suppose the state of a quantum system A, which we wish to copy, is ( see bra-ket notation ).
Suppose we wish to deny that we can understand what an actual infinity is, and therefore we cannot understand what ( God's ) eternity is.
Suppose we wish to find the maximum likelihood estimate of β for a single observed value x.
Suppose we wish to evaluate
Suppose we wish to maximize subject to the constraint.
Suppose we wish to find the discrete probability distribution on the points with maximal information entropy.
Suppose, however, that we have some matrix Q that is not a pure rotation — due to round-off errors, for example — and we wish to find the quaternion q that most accurately represents Q.
Suppose we wish to determine if n = 221 is prime.
Suppose you are training your own classifier, and you wish to measure its performance using the well-accepted metrics of sensitivity and specificity.
The procedure is as follows: Suppose that and that we wish to compute.
Suppose that we have that Γ and H prove C, and we wish to show that Γ proves H → C.
Suppose we wish to find the expected value of the function
Suppose we wish to determine if n = 221 is prime.
Suppose two parties A and B wish to communicate in the following manner: A performs measurement on an observable and communicates the measurement outcome to B classically.
: Suppose you wish to predict the weather for Saturday, and you have some model that predicts Saturday's weather, given the weather of each day in the week.
Suppose we wish to measure the position of a particle to within an accuracy Δx.
Suppose that we are given two conditional probabilities, P ( X | A ) and P ( X | B ), and we wish to estimate P ( X | A, B ), the probability of event X given both conditions A and B.
Suppose we wish to assess the probability of guilt of a defendant in a court case in which DNA ( or other probabilistic ) evidence is available.
Suppose we have a set of English text documents and wish to determine which document is most relevant to the query " the brown cow ".
Suppose and .
`` Suppose you take Mr. Hearst's morning American at $10,000 a year '', Brisbane proposed.
Suppose John Jones, who, for 1960, filed on the basis of a calendar year, died June 20, 1961.
Here's how the scheme works: Suppose the operator pulls the lever to clear a particular signal.
Suppose that the minimal polynomial for T decomposes over F into a product of linear polynomials.
Suppose Af crosses C when Af.
Suppose Af is defined in the sub-interval Af.
Suppose that Af, and that the average operation requires only Af sec..
Suppose, he says, that the tables were turned, and we were in the Soviets' position: `` There would be more than 2,000 modern Soviet fighters, all better than ours, stationed at 250 bases in Mexico and the Caribbean.
`` Suppose you tell me the real reason '', he drawled.
Suppose, says Dr. Lyttleton, the proton has a slightly greater charge than the electron ( so slight it is presently immeasurable ).
`` Suppose you let me explain.
`` Suppose it was not us that killed these aliens.
Suppose it is something right on the planet, native to it.
Suppose we have sample space.
Suppose a chain consists of squares 8D, 8E, and 8F.
Suppose there is a chain at 1A, 2A, 3A, and 4A, along with another chain at 6A and 7A.
If two players tie for minority, they will share the minority shareholder bonus. Suppose Festival is the chain being acquired.
Alex is the majority shareholder, and Betty is the minority shareholder. Suppose now that Worldwide is the chain being acquired.
Suppose that R ( x, y ) is a relation in the xy plane.
Take as an example a program that looks up a specific entry in a sorted list of size n. Suppose this program were implemented on Computer A, a state-of-the-art machine, using a linear search algorithm, and on Computer B, a much slower machine, using a binary search algorithm.
) Then X < sub > i </ sub > is the value ( or realization ) produced by a given run of the process at time i. Suppose that the process is further known to have defined values for mean μ < sub > i </ sub > and variance σ < sub > i </ sub >< sup > 2 </ sup > for all times i. Then the definition of the autocorrelation between times s and t is
0.307 seconds.