Mathematics

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 =-

Mathematics, Advanced Math / By

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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.

Mathematics, Advanced Math / By

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 »

a. Employ numerical summary measures to characterize the changes in homeownership rates across the country during this period. b. Do the trends appear to be uniform across the U.S. or are they unique to certain regions of

Mathematics, Probability and Statistics / By

The file P02_51.xlsx contains data on U.S. homeownership rates. a. Employ numerical summary measures to characterize the changes in homeownership rates across the country during this period. b. Do the trends appear to be uniform across the U.S. or are they unique to certain regions of the country? Explain. EXPERT ANSWER a. Considering the problem containing …

a. Employ numerical summary measures to characterize the changes in homeownership rates across the country during this period. b. Do the trends appear to be uniform across the U.S. or are they unique to certain regions of Read More »

each sample of water has a 10% chance of containing a particular organic pollutant. assume that the samples are independent with regard to the presence of the pollutant. Find the probability that in the next 18 samples, exactly 2 contains the pollutant. (a) P(x

Mathematics, Probability and Statistics / By

each sample of water has a 10% chance of containing a particular organic pollutant. assume that the samples are independent with regard to the presence of the pollutant. Find the probability that in the next 18 samples, exactly 2 contains the pollutant. (a) P(x 4) (b) P(x 4) (c) P(3 x 7) EXPERT ANSWER

Suppose our stream consists of the integers 3, 1, 4, 1, 5, 9, 2, 6, 5. Our hash functions will all be of the form h(x) = ax+b mod 32 for some a and b. You should treat the result as a 5-bit binary integer. Determine the tail length for each stream element and the resulting estimate of the number of distinct elements if the hash function is

Mathematics, Other Math / By

Suppose our stream consists of the integers 3, 1, 4, 1, 5, 9, 2, 6, 5. Our hash functions will all be of the form h(x) = ax+b mod 32 for some a and b. You should treat the result as a 5-bit binary integer. Determine the tail length for each stream element and the …

Suppose our stream consists of the integers 3, 1, 4, 1, 5, 9, 2, 6, 5. Our hash functions will all be of the form h(x) = ax+b mod 32 for some a and b. You should treat the result as a 5-bit binary integer. Determine the tail length for each stream element and the resulting estimate of the number of distinct elements if the hash function is Read More »

1 -3 2 -6 If T is defined by T(x)=Ax, find a vector x whose image under T is b, and determine whether x is unique. Let A-| 0 1-2 | and b-1-26 5-16 10 Find a single vector x whose image under T is b

Mathematics, Advanced Math / By

EXPERT ANSWER 6 . Let the pre-image of (-6,-26,-2)T be x = (a,b,c)T where a,b, c are arbitrary real numbers. Then T(x) =Ax = (-6,-26,-2)T or, (a-3b+2c, b-2c, 5a-16b+10c)T = (-6,-26,-2)T . Hence, a-3b+2c = -6 …(1), b-2c = -26…(2) and 5a-16b+10c= 10…(3). The augmented matrix of the above linear system of equations is M (say)= 1 -3 2 -6 …

1 -3 2 -6 If T is defined by T(x)=Ax, find a vector x whose image under T is b, and determine whether x is unique. Let A-| 0 1-2 | and b-1-26 5-16 10 Find a single vector x whose image under T is b Read More »