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(Exponential martingales) Suppose O(t,w) = (01(t, w),...,On(t,w)) E R" with Ox(t,w) E VIO, T] for k = 1,..., n, where T < 0o. Define 2. = exp{ jQ1, wydBlo) – 4 640,w.do}osist where B(s) ER" and 62 = 0 . 0 (dot product). a) Use Ito's formula to prove that d24 = 2:0(t,w)dB(t). b) Deduce that 24 is a martingale for t <T, provided that Z40x(t,w) € V[O,T] for 1 sk sn.
w 23 yes pod som i 500.000 How your tum What mount stated her 25 years the forests 30 per year? GLP
..13 Extra syntheses HO . ~ — m . ^ — Vio eu no comm (2 separate syntheses)
A=Vio . How long will it take $250 to double at 2% compounded quarterly? D ih
E5.1 a) What is Som for ice at 273K? What is Som for water at 273K? b) What is Acewt a73K? b) What is ASnice swater at 273K? ice->water C ice->water
E5.1 a) What is Som for ice at 273K? What is Som for water at 273K? b) What is Acewt a73K? b) What is ASnice swater at 273K? ice->water C ice->water
The transfer function (w(s) (va (s)) of the DC motor shown in the figure is:* DS (2 Points) ialt) Ra w w(t) valt) vio, da
i got 3.98 uF
& Determine the capacitance between pauts A and B: ESHTE E Vio Heros value fitores suf and
2) a) Let w = xdy - ydx and j:M - RP the inclusion of a bounded region with regular boundary am. Show that the area of M is given by (1/2) Som j*w. b) Let w= xdy dz - ydx dz + zdx A dy and j:M CRP the inclusion of a bounded region with regular boundary am. Show that the volume of M is given by (1/3) Som j*w.
1. Compute and plot the curves of ip vs. vps for an FET with Vio-2.5V and K-1 mA/V2 for Vos-2V, 4V, 6V, and 8V for 0<VDs<6V. Label the triode region, the saturation region, as well to" GS as the boundary between the two.
1. Compute and plot the curves of ip vs. vps for an FET with Vio-2.5V and K-1 mA/V2 for Vos-2V, 4V, 6V, and 8V for 0
Som 5m Oo es shown Located as shoun