11.08.2013 Views

Slika - Shrani.si

Slika - Shrani.si

Slika - Shrani.si

SHOW MORE
SHOW LESS

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

A. Juriˇ<strong>si</strong>ć in V. Batagelj: Verjetnostni račun in statistika 223<br />

✬<br />

✫<br />

Gostota zvezne pogojne porazdelitve<br />

Naj bosta gostoti p(x, y) in pY (y) zvezni ter pY (y) > 0. Tedaj je<br />

FX(x|y) = lim<br />

h→0<br />

F (x,y+h)−F (x,y)<br />

h<br />

FY (y+h)−FY (y)<br />

h<br />

oziroma, če vpeljemo pogojno gostoto<br />

=<br />

pX(x|y) =<br />

tudi FX(x|y) = x<br />

−∞ pX(u|y) du .<br />

∂F<br />

∂y<br />

F ′ Y<br />

(x, y)<br />

(y) = 1<br />

pY (y)<br />

p(x, y)<br />

pY (y) ,<br />

V primeru dvorazseˇzne normalne porazdelitve dobimo<br />

pX(x|y) : N(µx + ρ σx<br />

<br />

(y − µy), σx 1 − ρ2 ).<br />

Univerza v Ljubljani ▲<br />

❙ ▲<br />

▲<br />

σy<br />

x<br />

−∞<br />

p(u, y)du<br />

● ❙ ▲<br />

▲<br />

☛ ✖<br />

▲<br />

✩<br />

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!