PROBABILITY

2. Given the following table

answer each of the questions.

Find µ_X and σ_X .

Given that

                          Y = -X+2

find µ_Y and σ_Y .

2B. Suppose that in the game of AFL the mean total number of points per match is 185 with a standard deviation of 33. Suppose that a season involves 202 matches. If the total points are normally distributed then answer the following questions.

1. How many games do you expect to have less than 100 points scored in them in a given season?

2. How many games do you expect to have between 200 and 220 points scored in them in a season?

3. How many points should be needed for a match to be in the top 5% of high scoring matches?

4. If a match is one of the bottom 5 lowest scoring matches of the season, what is an upper bound on what you expect the score to be?

2C. Suppose that asteroid impacts on the earth are modelled with a Poi-son distribution. Asteroids of diameter 4m are estimated to enter the Earth’s atmosphere once per year. Asteroids of diameter 1km are estimated to impact the Earth once every 500,000 years.

1. What is the probability of exactly 2 asteroids of 4m diameter entering the atmosphere in a 6 month period?

2. How many years are required for the probability of at least one 1km diameter impact to exceed 1%?

Use the above information from the tables to work out the following missing entries, and then calculate the company’s return on equity. Note: Turnover and the average collection period are calculated using start-of-year, not average, values. (Enter your answers in millions. Round intermediate calculations and final answers to 2 decimal places.)

3/26

1 mo 0.01

6 mo 0.04

1 yr 0.13

2 yr 0.3

3 yr 0.36

5 yr 0.51

3/27

1 mo 0.01

6 mo 0.02

1 yr 0.11

2 yr 0.25

3 yr 0.3

5 yr 0.41

1. It is March 26 and you hold a $1mm (market value) long position in the 1-yr zero-coupon bond. Using modied durations, determine how much of the 5-yr zero-coupon bond you need to short so that your portfolio remains approximately unchanged if the 1-yr and 5-yr zero rates move in parallel.

2. What would the change in your portfolio value be if both the 1-yr rate and the 5-yr rate go up by 2 basis points?

3. What would the change in your portfolio value be if both the 1-yr rate and the 5-yr rate go down by 2 basis points?

4. What would the change in your portfolio value be if the 1-yr rate goes down by 2 basis points but the 5-yr rate stays the same?

5. What actually happens the following day? Calculate the value of your portfolio. Why did your portfolio value change from before?

Long-term debt ratio 0.3 Times interest earned 8.0 Current ratio 1.4 Quick ratio 1.0 Cash ratio 0.4 Inventory turnover 4.0 Average collection period 73 days Use the above information from the tables to work out the following missing entries, and then calculate the company’s return on equity. Note: Turnover and the average collection period are calculated using start-of-year, not average, values. (Enter your answers in millions. Round intermediate calculations and final answers to 2 decimal places.)

COMPLETE THE INCOME STATEMENT

Net Sales?

Cost of Goods sold?

selling, general and administrative expenses = 16.00

depreciation = 26.00

EBIT?

Interest Expense?

income before tax?

tax (35% of income before tax)?

Net Income?

COMPLETE THE BALANCE SHEET

Balance Sheet
Figures in Milliions    this year last year
Assets
Cash and marketable securities ? $26
accounts receivable ? 40
inventories ? 32
Total current assets ? $98
net property, plant, and equipment ? $129
Liabilities and shareholders equity
Accounts payable $20.00 $15
Notes payable 30 $35
total current liabilities ? $50
long term debt ? $26
shareholders equity ? $53
total liabilities and shareholders equity $175.00 $129

An investor is reviewing two proposals, assuming similar risk profiles and a 14% required return, which one should the investor buy? Why?

Lee Vista:

Purchase Price: $464,000

Cash flows from operations:

Year 1 $48,000

Year 2 $49,440

Year 3 $50,923

Year 4 $52,451

Year 5 $54,025

Cash flow from sale on year 5 $560,000

Colony Park:

Purchase Price: $500,000

Cash flows from operations:

Year 1 $56,000

Year 2 $57,400

Year 3 $58,835

Year 4 $60,306

Year 5 $61,814

Cash flow from sale on year 5 $597,000

Where are the deer? Random samples of square-kilometer plots were taken in different ecological locations of a national park. The deer counts per square kilometer were recorded and are shown in the following table.

A)  Find SS_TOT, SS_BET, and SS_W and check that SS_TOT = SS_BET + SS_W. (Use 3 decimal places.)

B) Find d.f._BET, d.f._W, MS_BET, and MS_W. (Use 4 decimal places for MS_BET, and MS_W.)

C) Find the value of the sample F statistic. (Use 2 decimal places.)

Margot is walking in a straight line from a point 40 feet due east of a statue in a park toward a point 34 feet due north of the statue. She walks at a constant speed of 4 feet per second.

(a) Write parametric equations for Margot's position t seconds after she starts walking. (Round your coefficients to four decimal places as needed.)

(b) Write an expression for the distance from Margot's position to the statue at time t. (Round your coefficients to four decimal places as needed.)

(c) Find the times when Margot is 36 feet from the statue. (Round your answers to two decimal places)