Given two independent uniform random variables U1 and U2 both with parameters [0,1],

1) Calculate the probability that 0.3 <= X + Y <= 0.8

2) Calculate the PDF of X+Y

3) Calculate the PDF of X-Y

Using excel with formulars

for binomial random variable X with n=10, p=0.3, plot its pdf and cdf; then simulate from it a sample of size N=2000, plot its histogram (relative frequency), and cumulative frequency.

firm’s stock has a 0.2 possibility to make 40.00% return, a 0.50 chance to make 10% return, and a 0.3 possibility to make -10% return. Calculate standard deviation

a.   0.03

b.   0.04

c.   0.05

d.   0.06

For a sex-linked gene at which there are two alleles, A1 and A2, in a population and for which the frequency of A1 is 0.9 in females and 0.3 in males, what will be the frequency of the A1 allele in the male offspring (sons) after one generation of random mating?

1. Which of the following statements correctly describes the short-term response towards a reduction in wealth.

   		The FE curve stays unchanged
   		The FE curve shifts to the right
   		The FE curve shifts to the left
   		None of the above

0.3 points   

QUESTION 10

1. Which of the following statements correctly describes the short-turn response towards an increase in current output

   		The IS curve stays unchanged
   		The IS curve shifts to the right
   		The IS curve shifts to the left
   		None of the above

0.3 points   

QUESTION 11

1. Which of the following statements correctly describes the short-turn response towards a decrease in lump-sum taxes, assuming that households are myopia and do not expect the future tax increase.

   		The IS curve stays unchanged
   		The IS curve shifts to the right
   		The IS curve shifts to the left
   		None of the above

Caro Manufacturing has two production departments, Machining and Assembly, and two service departments, Maintenance and Cafeteria. Direct costs for each department and the proportion of service costs used by the various departments for the month of August follow: Proportion of Services Used by Department Direct Costs Maintenance Cafeteria Machining Assembly Machining $ 115,000 Assembly 80,000 Maintenance 49,000 — 0.3 0.4 0.3 Cafeteria 33,000 0.6 — 0.2 0.2 Required: Use the step method to allocate the service costs, using the following: a. The order of allocation starts with Maintenance.(Negative amounts should be indicated by a minus sign. Do not round intermediate calculations.) b. The allocations are made in the reverse order (starting with Cafeteria).(Negative amounts should be indicated by a minus sign. Do not round intermediate calculations.)

1. Consider two farmers, one who owns land and the other who rents it from someone else. In good times (which happen with probability 0.3), the owner-farmer earns an income of 125. In bad times (which happen with probability 0.7), he earns an income of 75. The tenant works on a farm that is twice as large and earns an income of 250 in good times (prob=0.3) and 150 in bad times (prob=0.7).

   1. However, he must pay a rent of 100. Calculate the expected net income of both farmers.

   2. Assume that their utility function takes the following form: ? = ?1/2, where ?stands for the farmer’s net income. Calculate the expected utility of both.

   3. Compare this result to the calculation on expected income. What do you conclude in terms of the different risks that both farmers face?

A simple economy consists of two industries: agriculture and manufacturing. The production of 1 unit of agricultural products requires the consumption of 0.2 unit of agricultural products and 0.3 unit of manufactured goods. The production of 1 unit of manufactured goods requires the consumption of 0.4 unit of agricultural products and 0.3 unit of manufactured goods.

(a) Find the total output of goods needed to satisfy a consumer demand for $120 million worth of agricultural products and $170 million worth of manufactured goods. (Round your answers to one decimal place.)

answer is wrong

(b) Find the value of the goods consumed in the internal process of production in order to meet the gross output. (Round your answers to one decimal place.)

Caro Manufacturing has two production departments, Machining and Assembly, and two service departments, Maintenance and Cafeteria. Direct costs for each department and the proportion of service costs used by the various departments for the month of August follow:

Required:

Use the reciprocal method to allocate the service costs. (Matrix algebra is not required.) (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Round your final answers to the nearest whole dollar amounts.)

Cost allocation to:

From: Maintenance Cafeteria Machining Assembly

Service department costs

Maintenance

Cafeteria

Total $ $ $ $

, we are given a set of n items. Each item weights between 0 and 1. We also have a set of bins (knapsacks). Each bin has a capacity of 1, i.e., total weight in any bin should be less than 1. The problem is to pack the items into as few bins as possible. For example Given items: 0.2, 0.5, 0.4, 0.7, 0.1, 0.3, 0.8 Opt Solution: Bin1[0.2, 0.8], Bin2[0.5, 0.4, 0.1], Bin3[0.7, 0.3] Each item must be placed in a bin before the next item can be pro- cessed. This problem is NP-hard. Give an approximation algorithm to solve the bin packing problem. Provide pseudo-code, time complexity analysis and proof of performance ratio.