Suppose that a set of three traffic lights along one section of road operate independently (i.e., no communication or special timing between the lights). Since this is a fairly main road, the lights are green with a probability of 0.7 and red with probability 0.3. As you go through this stretch of road, What's the probability that :

At least one of the lights is red?

Males and females are observed to react differently to a given set of circumstances. It has been observed that 70% of the females react positively to these circumstances, whereas only 40% of males react positively. A group of 20 people, 15 female and 5 male, was subjected to these circumstances, and the subjects were asked to describe their reactions on a written questionaire. A response picked at random from the 20 was negative. what is the probability that it was that of a male?(using bayes' rule)

An ideal gas is contained in a piston-cylinder device and undergoes a power cycle as follows: 1-2 isentropic compression from an initial temperature T1 5 208C with a compression ratio r 5 5 2-3 constant pressure heat addition 3-1 constant volume heat rejection The gas has constant specific heats with cv 5 0.7 kJ/kg·K and R 5 0.3 kJ/kg·K. (a) Sketch the P-v and T-s diagrams for the cycle. (b) Determine the heat and work interactions for each pro- cess, in kJ/kg. (c) Determine the cycle thermal efficiency. (d) Obtain the expression for the cycle thermal efficiency as a function of the compression ratio r and ratio of specific heats k.

Table 1: X    P(X) Table 2: X    P(X)              Table 3:   X    P(X)

               25     0.1                           25     -0.6                        25        0.5

              50      0.7                           50    0.2                            50      0.3

              75     0.2                            15    0.1                            75       0.1

              100   0.4                            100    0.1                          100    0.1

Consider the following information regarding the performance of a money manager in a recent month. The table represents the actual return of each sector of the manager’s portfolio in column 1, the fraction of the portfolio allocated to each sector in column 2, the benchmark or neutral sector allocations in column 3, and the returns of sector indices in column 4.

a-1. What was the manager’s return in the month?

a-2. What was her overperformance or underperformance?

b. What was the contribution of security selection to relative performance?

c. What was the contribution of asset allocation to relative performance?

2. The accompanying data table show the percentage of tax returns filed electronically in a city from 2000 to 2009. Complete the parts below.

Year   Percentage
2000   27
2001   29
2002   35
2003   42
2004   45
2005   49
2006   55
2007   59
2008   61
2009   67

​b) Calculate the MAD for the forecast in part a. ​(Round to two decimal places as​ needed.)

​d) Calculate the MAD for the forecast in part c (Round to two decimal places as​ needed.)

The following information is given for a stock. Investors assume that the return of the stock is best explained by a two-factor model that includes the market factor and a second risk factor. Using a dividend discount model, what is the price for this stock?

Stock covariance with the market= 0.5

Market variance = 0.25

Stock covariance with a second risk factor= 0.6

variance of the second factor= 0.3

Market Premium:3%

Second factor risk premium=1%

Risk free rate =2 %

Current earnings per share= $5,

The ROE is expected to shrink (decrease) at the rate 10% for first 5 years

The ROE is expected to grow at the rate 8% forever after the first 5 years

Payout for the first 5 years: 50%

Payout after 5 years: 50%

a. Suppose that the annual interest rate is 1% and no dividend will be declared for the index constituent stocks in the coming quarter. The index is currently standing at 25,500.

i. Compute the index futures deliverable in exact 3 months.

ii. Suppose now the dividend yield of the index constituent stocks is 0.3% rather than 0%. Without doing any calculation, explain whether the index futures price is higher or lower than your answer in part (i).

b. A silver futures contract requires the seller to deliver 5,000 Troy ounces of silver. Henry sells four July silver futures contract at a price of $16 per ounce. The initial margin is $6,000 per contract and the maintenance margin is $2,500 per contract. What is the futures price per ounce at which Henry would receive a margin call?

A biotech manufacturing company can make test kits at a cost of $ 20.00. Each “kit” for which there is a glove demand the week it is manufactured can be sold for $ 100.00. However, due to the short life of its components, each “kit” that cannot be sold during that week has to be discarded at a cost of $ 5.00

The weekly demand for that product is a random variable with the following pmf

a) Calculate the expected value of the demand for “kits” during one week

b) Calculate the variance of demand for a week

c) The company could manufacture 50 “kits” per shift. If they decide to go into business, how many shifts must they work (1, 2, or 3) to maximize the expected profit?

Assume you are given two resistors with resistances R1=4.0 kΩ and R2=6.0 kΩ and two capacitors with capacitances C1=4.0 µF and C2=6.0 µF.

a) Calculate the equivalent resistances Req and the equivalent capacitance Ceq if the resistors are connected in series and the capacitors are connected in parallel.

b) Now, use the Req and Ceq that you calculate in part (a) to construct an RC circuit. If an emf of 27 V is suddenly applied across Req and Ceq, calculate the current through the Req after t = 12 µs.

c) If the resistor R1 is made of iron wire with radius R= 3 mm, calculate the length of this wire. The resistivity of iron is ρiron= 9.68x10-8 Ω.m.

d) If the capacitance C2 has square parallel-plates with the separation of 0.3 mm, calculate the plate area A.

FINANCIAL ANALYSIS

Consider the following statistics (calculated based on simple ratios with only same year data and no averaging or past year data) to answer the questions:

Total Asset = $100,000, Working Capital ratio = 1.5:1, ROE = 22%, Gross Profit Margin = 15%, Quick ratio = 0.3:1, Cost of Goods Sold = $10,000; All other expenses = $5000

A) By showing working, state what is ROA?

B) By showing working state what is the debt ratio?

C) What is the net worth of the business?

D) By showing working, what is return on sales?

Comment on the following:

i) Profitability status

ii) Liquidity Status

iii) Inventory levels

iv) Current assets excluding inventory

v) Likely cash position