Then the joint distribution of X and Y is completely determined by our channel and by our choice of, the marginal distribution of messages we choose to send over the channel.

Then the joint distribution of is multivariate normal with mean vector and covariance matrix

Then they are independent, but not necessarily identically distributed, and their joint probability distribution is given by the Bapat – Beg theorem.

Then in 1946, the YPWW Department was combined with the Sunday School Department for joint conventions until 1951 when they were separated once again.

Then at the Amsterdam 1964 Interzonal, Bronstein scored very well, but only three Soviets could advance, by a FIDE rule, and he finished behind countrymen Smyslov, Mikhail Tal, and Boris Spassky, who finished as the joint winners, along with Larsen.

Then in the mid-1980s, Esalen entered into a joint publishing arrangement with Lindisfarne Press to publish a small library of Russian philosophical and theological books.

Then, the bill must be approved by the Congress, a special joint session of both houses ; alternatively, the bill can be submitted to a referendum.

Then the British Minister to Japan, Sir Rutherford Alcock, discussed with his treaty counterparts such as American Minister Robert Pruyn, the feasibility of a joint military strike against Takachika.

Then the joint Russo-French corps was to cross the Caspian Sea and land at the Iranian port of Astrabad.

Then in late summer 1992, he was assigned as leader of the negotiating team that traveled to Moscow to establish the framework for what subsequently became the ambitious and complex joint manned space program known as Shuttle / MIR.

Then start with the Ardaas with every word clear to all of the Sangat to make a joint prayer involving everyone present with all seriousness possible.

Then the joint posterior distribution of the probabilities p < sub > 1 </ sub >, ..., p < sub > m </ sub > is given by ;

Then, the joint distribution of and is

Then in 1842 the American Fur Company declared bankruptcy, and in order to continue in the trade Dousman entered into a joint venture with Rolette, Sibley, and Pierre Chouteau to organize a new company which would take its place on the upper Mississippi.

Then its expansion accelerated as an institution of higher education, especially after Kwansei Gakuin was under the joint control of MEC-S and the Canadian Methodist Church in 1911.

Then in 1996, the Carrizo Plain Management Partners again created a joint initiative called the Carrizo Plain Natural Area ( CPNA ) Plan.

Then U. S. President George W. Bush and then Danish Prime Minister, Anders Fogh Rasmussen, holding a joint press conference in the gardens of Marienborg, July 6 2005.

Then he places his other thumb bent so that the tip appears to be connected to the folded-down thumb with the forefinger bent to cover the joint.

Then the joint range of the quantities — that is, the range of the point — is the image of the hypercube by the affine map from to defined by.

Then the joint distribution of is spherically symmetric, up to a location shift.

Then follows a site investigation of soil, rock, fault distribution and bedrock properties on and below an area of interest to determine their engineering properties including how they will interact with, on or in a proposed construction.

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

Then Bernardo Bertolucci cast him in a small speechless role as a window upholsterer in the film La Luna which evaded American distribution due to its subject matter.

Then, the relativistic expression for the angular distribution of the bremsstrahlung ( considering only the dominant dipole radiation contribution ), is

Let be the mean of the values in associated with class c, and let be the variance of the values in associated with class c. Then, the probability of some value given a class,, can be computed by plugging into the equation for a Normal distribution parameterized by and.

Then the cevians are concurrent if and only if a mass distribution can be assigned to the vertices such that each cevian intersects the opposite facet at its center of mass.

Then, expensive video equipment was required: Laserdisc player, PC, genlock, and recording deck for producing the master ; subsequently two or more video decks were then needed for producing distribution copies.

Three books by Gurdjieff were published in the English language in the United States after his death: Beelzebub's Tales to His Grandson published in 1950 by E. P. Dutton & Co. Inc., Meetings with Remarkable Men, published in 1963 by E. P. Dutton & Co. Inc., and Life is Real Only Then, When ' I Am ', printed privately by E. P. Dutton & Co. and published in 1978 by Triangle Editions Inc. for private distribution only.

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

Then T has a chi-squared distribution with n − 1 degrees of freedom.

" Then, on May 14, 1861, " An act regulating the sale of prizes and the distribution thereof ," was also passed.

Then, the field radiated by the small source is a spherical wave which is modulated by the FT of the source distribution, as in eqn.

Then the phase space distribution determines the probability that the system will be found in the infinitesimal phase space volume.

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

Then, if n ≥ p, has a Wishart distribution with n degrees of freedom if it has a probability density function given by

Then, under the null hypothesis that M < sub > 2 </ sub > is the true model, the difference between the deviances for the two models follows an approximate chi-squared distribution with k-degrees of freedom.

Then, Boltzmann's entropy formula gives for the probability distribution function, A = const.

Then the theorem says that the asymptotic distribution of these invariants is uniform over the group, so that a conjugacy class with k elements occurs with frequency asymptotic to

Currently the organization dates from 2001 with a distribution in several types of units: combat units, response units ( unités d ' intervention ), unités de soutien et d ' appui et finally special reserve units as part of 3 joint military régions ( interarmees ) and the 10 military land sectors.

The company was named Associated Producers and was a joint venture between Hawks, Allan Dwan, Marshall Neilan and director Allen Holubar, with a distribution deal through First National.

In November 2006, Reilly's attorney presented to U. S. District Judge Susan Illston a letter from Hearst senior vice president James Asher to MediaNews President Jody Lodovic that said the two companies agreed to " offer national advertising and internet advertising sales for their San Francisco Bay area newspapers on a joint basis, and to consolidate the San Francisco Bay Area distribution networks of such newspapers ..." Illston, suggesting she had been misled by the companies when they said they had not been collaborating, issued a 14-page ruling forbidding Hearst and MediaNews from working together on national advertising sales or distribution.

This is often recalculated as the divergence from the product of the marginal distributions to the actual joint distribution:

This is not straightforward because the maximum difference between two joint cumulative distribution functions is not generally the same as the maximum difference of any of the complementary distribution functions.

For the special case where is a joint probability distribution and the loss function is the negative log likelihood a risk minimization algorithm is said to perform generative training, because can be regarded as a generative model that explains how the data were generated.

However, also widely accepted as part of the notion of perfectly competitive market are perfect information about price distribution and very quick adjustments ( whose joint operation establish the law of one price ), to the point sometimes of identifying perfect competition with an essentially instantaneous reaching of equilibrium between supply and demand.

* by supplying a rule for constructing a new random variable from other random variables whose joint probability distribution is known.

* Osteoarthritis – distinguished with X-rays of the affected joints and blood tests, age ( mostly older patients ), starting pain less than an hour, a-symmetric distribution of affected joints and pain worsens when using joint for longer periods.

From 1971 until the end of 1987, Warner's international distribution operations were a joint venture with Columbia Pictures, and in some countries, this joint venture also distributed films from other companies ( like EMI Films and Cannon Films in the UK ).

The distribution of profits by other forms of mutual organization also varies from that of joint stock companies, though may not take the form of a dividend.

At the joint request of the German authorities and the Strasbourg Comité de Secours, she superintended the supplying of work to the poor of Strasbourg in 1871, after the Siege of Paris, and in 1872 had charge of the public distribution of supplies to the destitute people of Paris.

The Kolmogorov extension proceeds along the following lines: assuming that a probability measure on the space of all functions exists, then it can be used to specify the joint probability distribution of finite-dimensional random variables.

This measure is also known as the joint probability distribution, the joint distribution, or the multivariate distribution of the random vector.

The fact that two random variables X and Y both have a normal distribution does not imply that the pair ( X, Y ) has a joint normal distribution.