A = { [1,2,3,2] , [-2,0,-2,-4], [0,4,4,0], [1,2,3,2]}
Can you answer the following questions regarding this matrix:
a) Find the null space of A
b) Find vectors v1,v2.... such that Null A = span {v1,v2...}
c) Is the null space of A subspace of R4
In: Advanced Math
CHAPTER 2-4
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(a) What is the expected return of investing 50% of the portfolio in asset A and 50% of the portfolio in asset B? What is the standard deviation of this return? |
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(b) Replace CORR(X, Y) = 0.30 by CORR(X, Y) = 0.60 and answer the questions in part (a). Do the same for CORR(X, Y) = 0.60, 0.30, and 0.0. |
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(c) (Spreadsheet Exercise). Use a spreadsheet to perform the following analysis. Suppose that the fraction of the portfolio that is invested in asset B is f, and so the fraction of the portfolio that is invested in asset A is (1 f). Letting f vary from f = 0.0 to f = 1.0 in increments of 5% (that is, f = 0.0, 0.05, 0.10, 0.15, . . . ), compute the mean and the standard deviation of the annual rate of return of the portfolio (using the original data for the problem). Notice that the expected return of the portfolio varies (linearly) from 0.15 to 0.20, and the standard deviation of the return varies (non-linearly) from 0.05 to 0.06. Construct a chart plotting the standard deviation as a function of the expected return. |
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(d) (Spreadsheet Exercise). Perform the same analysis as in part (c) with CORR (X, Y) = 0.30 replaced by CORR(X, Y) = 0.60, 0.0, 0.30, and 0.60. |
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Exercise 2.38
Ninety percent of residential gas customers in Illinois use gas for residential heating. Sixteen residential gas customers are randomly selected to participate in a panel discussion for a state energy fair. A gas industry executive is hopeful that at least twelve of the panel members, i.e., 75%, will come from homes in which gas is used for residential heating. If you were the executive's assistant, what degree of assurance could you give the executive that her 75% goal might be reached or exceeded?
In: Statistics and Probability
A group of 9 friends includes 4 Americans, 2 Canadians, and 3 Italians. Three friends are to be selected at random for a trip. Let X denote the number of Americans and Y be the number of Canadians selected at random among the three friends selected for a trip.
1) Find the joint probability density function of the random variables X and Y and the marginal density functions.
2) Find Cov(2X-1, -Y+1).
In: Statistics and Probability
Parramore Corp has $15 million of sales, $2 million of inventories, $4 million of receivables, and $2 million of payables. Its cost of goods sold is 75% of sales, and it finances working capital with bank loans at an 8% rate. Assume 365 days in year for your calculations. Do not round intermediate steps.
1. What is Parramore's cash conversion cycle (CCC)? Do not round intermediate calculations. Round your answer to two decimal places. _____ days
2. If Parramore could lower its inventories and receivables by 12% each and increase its payables by 12%, all without affecting sales or cost of goods sold, what would be the new CCC? Do not round intermediate calculations. Round your answer to two decimal places. ____days
3. How much cash would be freed up, if Parramore could lower its inventories and receivables by 12% each and increase its payables by 12%, all without affecting sales or cost of goods sold? Do not round intermediate calculations. Round your answer to the nearest cent. Write out your answer completely. For Example, 13.2 million should be entered as 13,200,000. $____
4. By how much would pretax profits change, if Parramore could lower its inventories and receivables by 12% each and increase its payables by 12%, all without affecting sales or cost of goods sold? Do not round intermediate calculations. Round your answer to the nearest cent. Write out your answer completely. For Example, 13.2 million should be entered as 13,200,000. $________
In: Finance
In a constant‑pressure calorimeter, 55.0 mL of 0.820 M H 2 SO 4 was added to 55.0 mL of 0.360 M NaOH . The reaction caused the temperature of the solution to rise from 23.45 ∘ C to 25.90 ∘ C. If the solution has the same density and specific heat as water ( 1.00 g / mL and 4.184 J / ( g ⋅ °C), respectively), what is Δ H for this reaction (per mole of H 2 O produced)? Assume that the total volume is the sum of the individual volumes.
In: Chemistry
In a constant‑pressure calorimeter, 60.0 mL of 0.920 M H 2 SO 4 was added to 60.0 mL of 0.360 M NaOH . The reaction caused the temperature of the solution to rise from 22.43 ∘ C to 24.88 ∘ C. If the solution has the same density and specific heat as water ( 1.00 g / mL and 4.184 J / ( g ⋅ °C), respectively), what is Δ H for this reaction (per mole of H 2 O produced)? Assume that the total volume is the sum of the individual volumes.
In: Chemistry
Hydrazine, N 2 H 4 , reacts with oxygen to form nitrogen gas and water. N 2 H 4 ( aq ) + O 2 ( g ) ⟶ N 2 ( g ) + 2 H 2 O ( l ) If 2.45 g of N 2 H 4 reacts with excess oxygen and produces 0.650 L of N 2 , at 295 K and 1.00 atm, what is the percent yield of the reaction?
In: Chemistry
Using Matlab, consider the function f(x) = x^3 – 2x + 4 on the interval [-2, 2] with h = 0.25. Write the MATLAB function file to find the first derivatives in the entire interval by all three methods i.e., forward, backward, and centered finite difference approximations.
Could you please add the copiable Matlab code and the associated screenshots? Thank you!
In: Computer Science
Consider the data set.
(a)
Find the range. (Enter an exact number.)
(b)
Use the defining formula to compute the sample standard
deviation s. (Enter a number. Round your answer to two
decimal places.)
(c)
Use the defining formula to compute the population standard deviation σ. (Enter a number. Round your answer to two decimal places.)
In: Statistics and Probability
4) i: There are many ways to measure and monitor your costs.
State 2.
ii: What is Tax Efficiency?
In: Accounting