8. Pepcico Inc. has a beta of 0.59. The risk-free rate is 2% and the market risk premium is 8%. What is the required rate of return of Pepcico? Round to the nearset hundredth percent. Answer in the percent format. Do not include % sign in your answer (i.e. If your answer is 4.33%, type 4.33 without a % sign at the end.)

7.

You are composing a two-stock portfolio consisting of 40 percent Stock X and 60 percent Stock Y. Given the following information, find the standard deviation of this portfolio.

Round to the nearset hundredth percent. Answer in the percent format. Do not include % sign in your answer (i.e. If your answer is 4.33%, type 4.33 without a % sign at the end.)

Lottery

One state lottery game has contestants select 5 different numbers from 1 to 45. The prize if all numbers are matched is 2 million dollars.   The tickets are $2 each.

1)    How many different ticket possibilities are there?

2)    If a person purchases one ticket, what is the probability of winning? What is the probability of losing?

3)    Occasionally, you will hear of a group of people going in together to purchase a large amount of tickets. Suppose a group of 30 purchases 6,000 tickets.

a)    How much would each person have to contribute?

b)    What is the probability of the group winning? Losing?

4)    How much would it cost to “buy the lottery”, that is, buy a ticket to cover every possibility? Is it worth it?

5)    Create a probability distribution table for the random variable x = the amount won/lost when purchasing one ticket.

6)    In fair games, the expected value will be $0. This means that if the game is played many…many times, then one is expected to break even eventually. This is never true for Casino and Lottery games.   Find the expected value of x = the amount won/lost when purchasing one ticket.

7)    Interpret the expected value. See section 4.2 in the textbook for an example on how to interpret the expected value.

8)    Fill in the following table using the expected value.

One state lottery game has contestants select 5 different numbers from 1 to 45. The prize if all numbers are matched is 2 million dollars.   The tickets are $2 each.

1)    How many different ticket possibilities are there?

2)    If a person purchases one ticket, what is the probability of winning? What is the probability of losing?

3)    Occasionally, you will hear of a group of people going in together to purchase a large amount of tickets. Suppose a group of 30 purchases 6,000 tickets.

a)    How much would each person have to contribute?

b)    What is the probability of the group winning? Losing?

4)    How much would it cost to “buy the lottery”, that is, buy a ticket to cover every possibility? Is it worth it?

5)    Create a probability distribution table for the random variable x = the amount won/lost when purchasing one ticket.

6)    In fair games, the expected value will be $0. This means that if the game is played many…many times, then one is expected to break even eventually. This is never true for Casino and Lottery games.   Find the expected value of x = the amount won/lost when purchasing one ticket.

7)    Interpret the expected value. See section 4.2 in the textbook for an example on how to interpret the expected value.

8)    Fill in the following table using the expected value.

One state lottery game has contestants select 5 different numbers from 1 to 45. The prize, if all numbers are matched is 2 million dollars. The tickets are $2 each.

1) How many different ticket possibilities are there?

2) If a person purchases one ticket, what is the probability of winning? What is the probability of losing?

3) Occasionally, you will hear of a group of people going in together to purchase a large amount of tickets. Suppose a group of 30 purchases 6,000 tickets. a) How much would each person have to contribute? b) What is the probability of the group winning? Losing?

4) How much would it cost to “buy the lottery”, that is, buy a ticket to cover every possibility? Is it worth it?

5) Create a probability distribution table for the random variable x = the amount won/lost when purchasing one ticket.

6) In fair games, the expected value will be $0. This means that if the game is played many…many times, then one is expected to break even eventually. This is never true for Casino and Lottery games. Find the expected value of x = the amount won/lost when purchasing one ticket.

7) Interpret the expected value. See section 4.2 in the textbook for an example on how to interpret the expected value.

8) Fill in the following table using the expected value.

Please answer all questions! I will rate you!

1. Fit a multiple linear regression model of the form y=β0 + β1 x1 + β2 x2 + β3 x3 + ε. Here, ε is the random error term that is assumed to be normally distributed with 0 mean and constant variance. State the estimated regression function. How are the estimates of the three regression coefficients interpreted here? Provide your output, and interpretations in a worksheet titled “Regression Output.”
2. Obtain the residuals and prepare a box-plot of the residuals. What information does this plot provide? Provide your output, and interpretations in a worksheet titled “Box Plots Residuals.”
3. Plot the residuals against the predicted value of y, x1, x2, and x3. Also prepare a normal probability plot. Interpret the plots and summarize your findings. Provide your output, and interpretations in a worksheet titled “Residuals Plots”
4. Calculate the Variance Inflation Factors for the model. Comment on the findings with respect to the multicollinearity assumption. Provide your output, and interpretations in a worksheet titled “Multicollinearity.”

Calculate annual arithmetic rate of return and annual geometric rate of return of stock A and B. Consider the data in table below, which show the movements in price for two stocks over two successive holding periods. Both stocks have a beginning price of $10. Stock A rises to $40 in period 1 and then declines to $30 in period 2. Stock B falls to $8 in period 1 and then rises to $25 in period 2.

4. (Applying LU and LUP decompositions) In this problem, we'll use the LU/LUP decomposition to solve a linear system of equations.

a) For A = [12 -8 13 -1 13;14 11 -5 -5 -7;1 -8 -9 10 8;-11 10 -8 3 8;-11 -8 4 2 -4] find matrices P, L, and U so that PA = LU using Matlab's lu function. Based on your results: did Matlab use pivoting during the lu-computation?

b) For b = [4;-4;-5;3;7] solve Ax = b using the LU decomposition as follows. Solving Ax = b is the same as solving PAx = Pb. (With P from a). Since PA = LU, we need to solve LUx = Pb, and we can split that into two triangular systems as follows: Ly = Pb, and Ux = y. Solve both of these systems using Matlab's linsolve, state x and y explicitly.

c) Compare the quality of the x you found in b to the solution of Ax = b you get from using linsolve. (As in 2d, work with the differences Ax - b).

d) You want so solve Ax = b for various vectors b, so you collect them into a single matrix B. So your goal is to find a matrix X so that AX = B (one column in X for each column in B). Working with P, L, and U from parts a/b we see that this amounts to solving two systems: LY = PB and UX = Y. For B = [18 -7 -14 10 -14 -2 13 12 -15 -15;-15 -14 4 -2 13 -16 15 -3 -15 14;3 12 -10 -17 2 19 -17 17 15 5;-1 -8 6 -11 20 -20 -4 -13 3 -6;-20 1 8 17 -17 11 -10 -10 2 1] solve these two equations using Matlab's linsolve.

First find Y in LY = PB, and then use that to find X in UX = Y. Check that AX - B is close to the zero matrix.

For this last problem, work with format short (or even format compact) so that the matrices don't use up too much screenspace.

Traffic counts and signal timing data were collected for the intersection of Sand Creek Road and Wolf Road. The intersection is signalized. The collected data show that, for a particular cycle, vehicles on the through lane of the SB of Sand Creek Road had the following arrival headway pattern (counted from the start of the red time of the cycle):

– 2.5 seconds for the first 10 seconds

– 2 seconds for the time period of 44 ‐ 50 seconds, and for the time period of 130 ‐ 166 seconds

– No vehicle was observed in‐between of the above time periods.

– Collected data also show that the cycle length is 200 seconds with 140 seconds for the effective red time and 60 seconds for the effective green time. Assume the discharge headway after the signal turns green is 2 seconds. Ignore the interactions of vehicles from left‐ and right‐turn lanes when you conduct the analysis.

Find:

– Maximum queue size

– Maximum delay

– Total queuing delay

– Average queuing delay

he file Utility contains the electricity costs, in dollars, during July of a recent year for a random sample of 50 one-bedroom apartments in a large city: SELF TEST 96 171 202 157 185 90 141 149 206 95 163 150 108 119 183 178 147 116 172 175 123 154 130 151 114 102 153 111 148 128 144 143 187 135 191 197 127 82 213 130 165 168 109 167 166 139 149 137 129 158 Decide whether the data appear to be approximately normally distributed by a. comparing data characteristics to theoretical properties. b. constructing a normal probability plot.

Q8. One store notes that the probability of some type of error in a telephone order is 0.2. A supervisor randomly selects telephone orders and carefully inspects each one.

1. (2pts) What is the probability that the third telephone order selected will be the first to contain an error?

2. (3pts) What is the probability that the supervisor will inspect between two and six (inclusive) telephone orders before finding an error?

3. (3pts) What is the probability that the inspector will examine at least seven orders before finding an error?

4. (4pts) Suppose the first four telephone orders contain no errors, what is the probability that the first error will be on the eighth order or later?