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E x e c u t i v e s u m m a r y A l t h o u g h n ­ t i e r, m o n o l i t h i c a r ch i t e ct u r e s a r e t h e n o r m f o r m o st a p p l i ca t i o n s r uO p p o rt u n i t y t o se e k mo re su p p o rt vi a t h e UCS F Co p e P ro g ra m (t i n y u csf e d u / co p e ) (e g , " F e e l i n g st re sse d i s n o t a si g n o f we a kn e ss, i t i s n o rma l i n t h e se ci rcu mst a n ce s I wa n t t o sh a re so me re so u rce s t h a t mi g h t h e l pLet Y = g(X) where g R !R Then F Y(y) = P(Y y) = P(g(X) y) = Z A(y) p X(x)dx where A(y) = fx g(x) yg The density is p Y(y) = F0 Y (y) If gis strictly monotonic, then p Y(y) = p X(h(y)) dh(y) dy where h= g 1 Example 3 Let p X(x) = e x for x>0 Hence F X(x) = 1 e x Let Y = g(X) = logX Then F Y(y) = P(Y y) = P(log(X) y) = P(X e y) = F X(e Solutions To Linear Algebra Stephen H Friedberg Fourth Edition Chapter 2 ƒp[ƒ} ‹­‚ß ƒVƒ‡[ƒg ƒƒ"ƒY