Then Professor Marvin Zelen, a statistician and associate of the recently founded Committee for the Scientific Investigation of Claims of the Paranormal ( CSICOP, now known as the Committee for Skeptical Inquiry ( CSI )), proposed in a 1976 article in the same periodical that, in order to eliminate any demographic anomaly, Gauquelin randomly pick 100 athletes from his data-set of 2, 088 and check the birth / planet correlations of a sample of babies born at the same times and places in order to establish a control group, giving the base-rate ( chance ) expectation for comparison ( The 100 random athletes later expanded into a subsample of 303 athletes ).

Then we apply the law of total expectation to each term by conditioning on the random variable X:

Then a conditional expectation of X given is any-measurable function which satisfies:

Then the conditional probability given is a function such that is the conditional expectation of the indicator function for A:

Then the expectation in the first-stage problem's objective function can be written as the summation:

Then the Feynman – Kac formula tells us that the solution can be written as a conditional expectation

Then, if we let and be the expectation of, for any

Then, to find the expectation value of the Hamiltonian:

Then is the non-vanishing vacuum expectation value of the Higgs field.

Then the required information is collected from a simple random sample of the elements within each selected group.

Then simple random sampling or systematic sampling is applied within each stratum.

Then the random number of successes we have seen, X, will have the negative binomial ( or Pascal ) distribution:

Then the statistician must analyze the properties of and, which are viewed as random vectors since a randomly different selection of n cases to observe would have resulted in different values for them.

Then there is some probability distribution m on the interval and some random variable Y such that

Then under such a rotation, a random phase,, will be created between the eigenstates, of.

Then, each student ’ s score would be a realization of one of a set of independent and identically distributed random variables, with a mean of 50.

Then, a tail event is an event whose occurrence or failure is determined by the values of these random variables but which is probabilistically independent of each finite subset of these random variables.

Then, a particle is placed in a random position of the screen, and moved randomly until it bumps against the seed.

Then random " noise " words can not be used as successfully to fool the filter.

Then the Wishart distribution is the probability distribution of the p × p random matrix

Then a random selection is made similar to how the roulette wheel is rotated.

Then to commit to a bit b Alice picks a random input x and sends the triple

Then, Victor enters the cave and shouts the name of the path he wants her to use to return, either A or B, chosen at random.

Then, we add the segments from the subdivision, one by one, in random order, refining the trapezoidal decomposition.

Then, three of the elements would be selected at random, and then the therapist would ask :" In relation to … ( whatever is of interest ), in which way two of these people are alike but different from the third "?

Then a coupling of and is a new probability space over which there are two random variables and such that has the same distribution as while has the same distribution as.

are identically distributed random variables that are mutually independent and also independent of N. Then the probability distribution of the sum of i. i. d.

Then let the random variables X < sub > i </ sub > indicate the number of times outcome number i was observed over the n trials.

Then, we generate a random number for each of n trials and use a logical test to classify the virtual measure or observation in one of the categories.

Now let G be some graph, let v be a vertex of G, and let R be a random walk on G starting from v. Let T be some stopping time for R. Then the loop-erased random walk until time T is LE ( R ()).

Then the whole process would be repeated to eliminate another variable.

Then is already an angle variable, and the canonical momentum conjugate is L, the angular momentum.

Then Y < sub > i </ sub > can be viewed as an indicator for whether this latent variable is positive:

Then an equation expressing y as an implicit function of the other variable ( s ) can be written.

Then changing the system's temperature parameter by and the external variable by dx will lead to a change in:

Then, female and male would be the categories included under the Gender variable.

More precisely, let F be a field, and let F be the ring of polynomials in one variable, X, with coefficients in F. Then each f < sub > i </ sub > lies in F. ∂< sub > X </ sub > is the derivative with respect to X.

Then a Yule – Simon distributed variable K has the following geometric distribution conditional on W:

Then a random variable is called a stopping time if for all in.

More formally, let us use variable x to denote abusively the tuple of variables involved in statement S. Then, a given Hoare triple is provable in Hoare logic for total correctness if and only if the first-order predicate below holds:

Then integration by parts in each variable yields

Then, a graph. is plotted of the points that a particular value for the changed variable visits after transient factors have been neutralised.

Then Y can be viewed as an indicator for whether this latent variable is positive:

Then the null hypothesis of no Granger causality is retained if and only if no lagged values of an explanatory variable have been retained in the regression.

Then it selects randomly a variable, whose value conflicts with any constraint of the CSP.

Then it assigns to this variable the value with the minimum conflicts.

Then X < sub > a, b </ sub > is the a-th root of a suitably defined Beta distributed random variable.

For example, imagine pulling a numbered ball with the number k from a bag of n balls, numbered 1 to n. Then you could describe a likelihood function for the random variable N as the probability of getting k given that there are n balls: the likelihood will be 1 / n for n greater or equal to k, and 0 for n smaller than k. Unlike a probability distribution function, this likelihood function will not sum up to 1 on the sample space.

Then follows a long variable Benediction of four clauses, pronounced by the priest, the people responding " Amen " to each clause.

Then the random variable