II.D Many Random Variables
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چکیده
With more than one random variable, the set of outcomes is an N -dimensional space, Sx = {−∞ < x1, x2, · · · , xN < ∞}. For example, describing the location and velocity of a gas particle requires six coordinates. • The joint PDF p(x), is the probability density of an outcome in a volume element dx = ∏N i=1 dxi around the point x = {x1, x2, · · · , xN}. The joint PDF is normalized such that px(S) = ∫
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REQUESTED AMOUNT $ PROPOSED DURATION (1-60 MONTHS) months REQUESTED STARTING DATE SHOW RELATED PREPROPOSAL NO., IF APPLICABLE CHECK APPROPRIATE BOX(ES) IF THIS PROPOSAL INCLUDES ANY OF THE ITEMS LISTED BELOW BEGINNING INVESTIGATOR (GPG 1.A.3) DISCLOSURE OF LOBBYING ACTIVITIES (GPG II.D.1) PROPRIETARY & PRIVILEGED INFORMATION (GPG II.D.10) NATIONAL ENVIRONMENTAL POLICY ACT (GPG II.D.10) HISTORIC...
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REQUESTED AMOUNT $ PROPOSED DURATION (1-60 MONTHS) months REQUESTED STARTING DATE SHOW RELATED PRELIMINARY PROPOSAL NO. IF APPLICABLE CHECK APPROPRIATE BOX(ES) IF THIS PROPOSAL INCLUDES ANY OF THE ITEMS LISTED BELOW BEGINNING INVESTIGATOR (GPG I.G.2) DISCLOSURE OF LOBBYING ACTIVITIES (GPG II.C.1.e) PROPRIETARY & PRIVILEGED INFORMATION (GPG I.D, II.C.1.d) HISTORIC PLACES (GPG II.C.2.j) EAGER* (G...
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REQUESTED AMOUNT $ PROPOSED DURATION (1-60 MONTHS) months REQUESTED STARTING DATE SHOW RELATED PRELIMINARY PROPOSAL NO. IF APPLICABLE CHECK APPROPRIATE BOX(ES) IF THIS PROPOSAL INCLUDES ANY OF THE ITEMS LISTED BELOW BEGINNING INVESTIGATOR (GPG I.G.2) DISCLOSURE OF LOBBYING ACTIVITIES (GPG II.C.1.e) PROPRIETARY & PRIVILEGED INFORMATION (GPG I.D, II.C.1.d) HISTORIC PLACES (GPG II.C.2.j) EAGER* (G...
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REQUESTED AMOUNT $ PROPOSED DURATION (1-60 MONTHS) months REQUESTED STARTING DATE SHOW RELATED PRELIMINARY PROPOSAL NO. IF APPLICABLE CHECK APPROPRIATE BOX(ES) IF THIS PROPOSAL INCLUDES ANY OF THE ITEMS LISTED BELOW BEGINNING INVESTIGATOR (GPG I.A) DISCLOSURE OF LOBBYING ACTIVITIES (GPG II.C) PROPRIETARY & PRIVILEGED INFORMATION (GPG I.B, II.C.1.d) HISTORIC PLACES (GPG II.C.2.j) SMALL GRANT FOR...
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