Q1)California Surplus Inc. qualifies to use the installment-sales method for tax purposes and sold an investment on an installment basis. The total gain of $75000 was reported for financial reporting purposes in the period of sale. The installment period is 3 years; one-third of the sale price is collected in 2012 and the rest in 2013. The tax rate was 35% in 2012, and 30% in 2013 and 30% in 2014. The accounting and tax data is shown below.

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Homework #1 due Thursday January 17 1. Circles C and D meet at points A and B. The tangent to C at A meets D at a point P. Define Q to be any point of D inside C, and let S be the point where line BQ meets C. Prove that AS is parallel to PQ. For any diameter AA” of circle C = (O, r), let C1 = (O1, a) and C2 = (O2, a) be congruent circles, with a < r, that are internally tangent to C at A and A”, respectively. On the same side of AA” inside C we draw two more circles (O3, b) and (O4, c) externally tangent to one another and internally tangent to C, with the first circle tangent externally to C1 and the second to C2. Prove that (i) r = a + b + c, and (ii) O3O4 || AA”.

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Homework #1 Finding the Optimal State-Value Function Problem Description The game DieN is played in the following way: 1. You will be given a die with N sides. You will know the size of N, and can assume that N is a value greater than 1 and less than or equal to 30. 2. You will be given a bit mask vector isBadSide representing the sides of a die that will make you lose. The vector will be of size N, and 1 indexed. (there is no 0 side) 3. You start with 0 dollars. 4. At any time you have the option to roll the die or to quit the game a. If you decide to roll: i. And you roll a number not in isBadSide, you receive that many dollars. (eg. if you roll the number 2 and 2 is not active — meaning the second element of the vector is 0 — in isBadSide, then you receive 2 dollars) Repeat step 4. ii. And you roll a number in isBadSide, then you lose all money obtained in previous rolls and the game ends. b. If you decide to quit: i. You keep all money gained from previous rolls and the game ends. Procedure ● For this problem, determine an optimal policy for playing the game DieN for N sides. You will be given N and the array isBadSide which indicates which sides are bad. As you will see, the optimal policy for this game will depend on your current bankroll. ● You can try solving this problem either by creating an MDP of the game (state, action, transition, reward function, and assume a gamma of 1) and then calculating the optimal state-value function or you can plug-in values and solve directly using the Bellman Equations. ● What is the expected amount of dollars for this game if you follow an optimal policy? That is, what is the optimal state-value function for the initial state of the game? Provide answers for the problems you are given in the “Solve for Code” tab on the Heroku site. Your answer must be correct to 3 decimal places. Examples The following examples can be used to verify your calculation is correct. ● Input: N = 21, isBadSide = {1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,1,0,0,0,1,0}, Output: 7.3799 ● Input: N = 22, isBadSide = {1,1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0}, Output: 6.314 ● Input: N = 6, isBadSide = {1,1,1,0,0,0}, Output: 2.5833

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HOMEWORK 2

CS512 – Data Structures

Deadline

4 1 + 3 * 7 1 3 * 4 + –

7 4 + 2 * 8 3 * 4 – +

1.Enter elements into stack till operator is seen.Stack: 4, 1 +Add and push it onto stack:Stack: 5Stack: 5, 3 *Multiply and push it onto stack:Stack: 15Stack: 15, 7, 1, 3, *Multiply and…

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Suppose that a random sample of 200 twenty-year-old men is selected from a population and these men’s height (in inches), Hi , and weight (in pounds), Wi , are recorded. OLS estimation of a simple linear regression model relating weight to height yields the fitted regression model:

Wi = 25 + 1.75Hi

a) What is the regression’s weight prediction for someone who is 60inches tall?

b) A man has alate growth spurt and grows 2inches over the course of a year.  What is the regression’s prediction for the increase in this man’s weight?

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