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F (1)(x) = P(X (1)F Z(z) = P(Z z) = P(g(X;Y) z) = P(f(x;y) g(x;y) zg) = Z Z Az p X;Y(x;y)dxdy 3 The pdf is p Z(z) = F0 Z (z) Example 5 Practice problem Let (X;Y) be uniform on the unit square Let Z= X=Y Find the density of Z 5 Important Distributions Normal (Gaussian) X˘N( ;˙ 2) if p(x) = 1 ˙ p 2ˇ e (x )2=(2˙2 If X2Rd then X˘N( ;) if p(x) = 1 (2ˇ)d=2j j exp 1 2 (x )T 1(x ) Chisquared X3 2;cos2 ax (75) Z cosaxdx= 1 a sinax (76) Z cos2 axdx= x 2 sin2ax 4a (77) Z cos3 axdx= 3sinax Adapter Sony Nex E Nikon F Commlite Comix Cm Nf Nex Sklep Fotograficzny Krakow Foto Kram Pl ƒ‚ƒfƒ‹ƒnƒEƒX "„‹pƒZ[ƒ‹

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