Advanced Math

A more general and also complicated love between Romeo and Juliet is the IVP⎩⎨⎧​R˙=f(t,R,J),J˙=g(t,R,J),R(0)=R0​,J(0)=J0​,​wherefandgare two real functions dependent ont,R, andJ. Similarly, find conditions onfandgso that the IVP SYS. (14) has a solution. For example, a solution exists for IVP SyS. (14) wheref(R,J)=R(1−J)andg(R,J)=J(R−1)(this is also known as the Lotka-Volterra equations in Biology to model the interaction of two species). Give five specific examples of such IVPs without finding the exact solutions.

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36. Stock Prices of a Dividend Cycle In a discussion of stock prices of a dividend cycle, Palmon and Yaaril consider the function f given by (1 + r)l=2 ln(1 + r) u = f(t,r, z) = (1 + r)1–z – where u is the instantaneous rate of ask-price appreciation, r is an annual opportunity rate of return, z is the fraction of a dividend cycle over which a share of stock is held by a midcycle seller, and t is the effective rate of capital gains tax. They claim that ди t(1 + r)l-z In?(1 + r) [(1 + r)l–– t] Verify this. 37. Money Demand In a discussion of inventory theory of money demand, Swansonconsiders the function bᎢ , iᏟ F(b, C, T, i) + C 2 ƏF bT i and determines that + Verify this partial derivative. ac C2 2 az =-

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Two fair dice are thrown. Let A be the event the the first shows an odd number, B be the event that the second shows an even number, and C be the event the either both are odd or both are even.

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Two fair dice are thrown. Let A be the event the the first shows an odd number, B be the event that the second shows an even number, and C be the event the either both are odd or both are even. Show that A, B, C are pairwise independent, but not independent. Are A …

Two fair dice are thrown. Let A be the event the the first shows an odd number, B be the event that the second shows an even number, and C be the event the either both are odd or both are even. Read More »