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Page "Multivariate normal distribution" ¶ 90
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Then and joint
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 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 the joint distribution
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 and distribution
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

Then and is
Then he would get to his feet, as though rising in honor of his own remarkable powers, and say almost invariably, `` Gentlemen, this is an amazing story!!
Then, Jesus indicated that God's forgiveness is unlimited.
Certainly, the meaning is clearer to one who is not familiar with Biblical teachings, in the New English Bible which reads: `` Then Jesus arrived at Jordan from Galilee, and he came to John to be baptized by him.
Then it added: `` It is not possible to determine how extensive these ill effects will be -- nor how many people will be affected ''.
Then the words fell into a pattern: `` Mollie the Mutton is scratching her nose, Scratching her nose in the rain.
Then he thought of Aaron Blaustein standing in his rich house saying: `` God is tired of taking the blame.
Then it is marked on the inside where it comes in contact with the transom, frames, keelson and all the battens.
Then it is replaced and fastened.
Then the chines are rounded off and the bottom is rough-sanded in preparation.
Then, a group of eggs is deposited in a cavity in the beebread loaf and the egg compartment is closed.
Then there is a diagonalizable operator D on V and a nilpotent operator N in V such that ( A ) Af, ( b ) Af.
Then in 2 we show that any line involution with the properties that ( A ) It has no complex of invariant lines, and ( B ) Its singular lines form a complex consisting exclusively of the lines which meet a twisted curve, is necessarily of the type discussed in 1.
Then, too, the utmost clinical flexibility is necessary in judiciously combining carefully timed family-oriented home visits, single and group office interviews, and appropriate telephone follow-up calls, if the worker is to be genuinely accessible and if the predicted unhealthy outcome is to be actually averted in accordance with the principles of preventive intervention.
Then the editorial added prophetically: `` how far they may reach in Asia is yet undetermined, but they fall far short of our dreams of the war conferences ''.
Then she catapults into `` everything and everybody '', putting particular violence on `` everybody '', indicating to the linguist that this is a spot to flag -- that is, it is not congruent to the patient's general style of speech up to this point.
Then comes the time when the last wire is removed and Susie walks out a healthier and more attractive girl than when she first went to the orthodontist.
Then, with the new affluence, there is actually a sallying forth into the wide, wide world beyond the precincts of New York.
Then, if the middle number is activated to its greatest potential in terms of this square, through multiplying it by the highest number, 9 ( which is the square of the base number ), the result is 45 ; ;

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