If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.

If it were wholly random and unrelated, it would be 2.0, assuming the five classes were equal in n, which approximately they are.

If no address is provided, one is picked at random from the " base subnet ", 0.

If are independent and identically distributed random variables, each with a standard Cauchy distribution, then the sample mean has the same standard Cauchy distribution ( the sample median, which is not affected by extreme values, can be used as a measure of central tendency ).

If one watches a bacterium swimming in a uniform environment, its movement will look like a random walk with relatively straight swims interrupted by random tumbles that reorient the bacterium.

If it is moving in the wrong direction, it will tumble sooner and try a new direction at random.

If the affected bits are independently chosen at random, the probability of a two-bit error being undetected is 1 / n.

If we insert vertices in random order, it turns out ( by a somewhat intricate proof ) that each insertion will flip, on average, only O ( 1 ) triangles – although sometimes it will flip many more.

If a game has a board, the board is usually irregular rather than uniform or symmetric ( like Risk rather than chess or Scrabble ); the board is often random ( like Settlers of Catan ) or has random elements ( like Tikal ).

If X is a positive random variable and q > 0 then for all ε > 0

If μ is an unknown constant and W is random noise with probability density, then has probability density and is therefore a location family ..

If the degree of underrepresentation is small, the sample can be treated as a reasonable approximation to a random sample.

If the key is truly random, as large as or greater than the plaintext, never reused in whole or part, and kept secret, the ciphertext will be impossible to decrypt or break without knowing the key.

If a random experiment can result in N mutually exclusive and equally likely outcomes and if N < sub > A </ sub > of these outcomes result in the occurrence of the event A, the probability of A is defined by

If an individual coin toss or the roll of dice is considered to be a random event, then if repeated many times the sequence of random events will exhibit certain patterns, which can be studied and predicted.

If indeed an answer comes, the time and place it comes is considered random.

If X is a real-valued random variable and a is a number then the event X ≤ a is the set of outcomes whose corresponding value of X is less than or equal to a.

If is a vector-valued random variable, with values in, and thought of as a column vector, then the natural generalization of variance is, where and is the transpose of, and so is a row vector.

If is a complex-valued random variable, with values in, then its variance is, where is the conjugate transpose of.

If the attacker is spoofing source addresses randomly, the backscatter response packets from the victim will be sent back to random destinations.

If the response variable is expected to follow a parametric family of probability distributions, then the statistician may specify ( in the protocol for the experiment or observational study ) that the responses be transformed to stabilize the variance.

If we define the function f ( n ) = A ( n, n ), which increases both m and n at the same time, we have a function of one variable that dwarfs every primitive recursive function, including very fast-growing functions such as the exponential function, the factorial function, multi-and superfactorial functions, and even functions defined using Knuth's up-arrow notation ( except when the indexed up-arrow is used ).

If the heuristic can't find the correct setting, the variable is assigned randomly.

If X is Cauchy distributed with median μ and scale parameter γ, then the complex variable

If is a wrapped Cauchy distribution with the parameter representing the parameters of the corresponding " unwrapped " Cauchy distribution in the variable y where, then

If the density of the chain is variable then the analysis above can be adapted to produce equations for the curve given the density, or given the curve to find the density.

#: If, replace in above rules with some new variable and add rule.

If a Diophantine equation has as an additional variable or variables occurring as exponents, it is an exponential Diophantine equation.

If not, the null hypothesis is supported ( or, more correctly, not rejected ), meaning no effect of the independent variable ( s ) was observed on the dependent variable ( s ).

If I told you my son's age, then there would no longer be two unknowns ( variables ), and the problem becomes a linear equation with just one variable, that can be solved as described above.

The evidence was compiled by W de Sitter ( 1927 ) who wrote " If we accept this hypothesis, then the ' astronomical time ', given by the earth's rotation, and used in all practical astronomical computations, differs from the ' uniform ' or ' Newtonian ' time, which is defined as the independent variable of the equations of celestial mechanics ".

" If a dependent variable takes a while to fully absorb a shock.

If the primary variable is mass fraction (, given, for example, in ), then the equation changes to:

If our freshness condition is not met, then we may simply alpha-rename with a suitably fresh variable.

# If x is a variable, then x ∈ Λ

# If x is a variable and M ∈ Λ, then ( λx. M ) ∈ Λ

* If the price is between average total cost and average variable cost at the profit-maximizing output, then the firm is said to be in a loss-minimizing condition.

* If the price is below average variable cost at the profit-maximizing output, the firm should go into shutdown.

If the generalized coordinates are represented as a vector and time differentiation is represented by a dot over the variable, then the equations of motion ( known as the Lagrange or Euler – Lagrange equations ) are a set of equations:

If the revenue the firm is receiving is greater than its total variable cost ( R > VC ) then the firm is covering all variable cost plus there is additional revenue (" contribution "), which can be applied to fixed costs.

If the type declaration on the first line were omitted, the program would trigger an error on compilation, as the variable " p " would not be defined.

If the negated query can be refuted, it follows that the query, with the appropriate variable bindings in place, is a logical consequence of the program.