Consider an M / M / 1 queueing system with capacity N = 1, arrival rate λ = 0.2 customers per minute, and service rate µ =0.3 customers per minute. Let X(t) be the number of customers present at time t.

a) Suppose that X(0) =0. Calculate P{X(1) = 0} and P{X(10) = 0}

b) Suppose that X(0) =1. Calculate P{X(1) = 0} and P{X(10) = 0}

c) Could you have predicted the difference between the answers in part a, and part b by the general theory of limiting probabilities?

Suppose the risk free rate is 4%, the expected rate of return is 8% and the variance of a portfolio is estimated as 500%. What is the slope of the Capital Allocation Line? Interpret the meaning of your estimation of the slope. [see p.168 of your text]

Imagine that the expected returns that are associated with an investment are 0.06, 0.08, 0.094, 0.12 and 0.134. If the standard deviations that are associated with the returns are 0, 0.022, 0.066, 0.154, and 0.176 respectively, what is the investor’s utility function? [see p. 159, pp.170-171 of your text]

Plot the utility function of the investor on a scale of 0, 0.1, 0.2, 0.3, and 0.4 for additional credit.

:    A concert promoter needs to decide how many concert T- shirt to order supplied with          its logo name on the front side of T-shirt. The profit on each one sold at the concert is 50 L.E. and any unsold T-shirt and returned to the supplied company will cause a loss of 30 L.E for the promoter. Demand is uncertain but is estimated to be between 200 to 1000 T-shirt. The probabilities of different demand levels are as follows:

Demand Level             200             400            600           800       

       Probability              0.2               0.3               0.4           0.1

How many T-shirt should the promoter order to get the higher profit and the least loss?

You have a two stock portfolio with $3,000 in stock A and $7,000 in stock B. You believe the following probability distribution exists for your stocks.

1. Calculate Expected rate of Return, Risk, and CV of Stock A

2. Calculate portfolio expected rate of return, portfolio risk , and portfolio CV. Note: expected rate of Return , risk, and CV of Stock B are 16,7, and 0.44 respectively .

In a town, 36% of the citizens contributed to the Republicans, 46% contributed to the Democrats, and 12% contributed to both. What percentage contributed to neither party?

A box contains 4 white, 3 red, and 3 black marbles. One marble is chosen at random, and it is not black. Find the probability that it is white. (Enter your answer as a fraction.)

Suppose that 90% of drivers are "careful" and 10% are "reckless." Suppose further that a careful driver has a 0.2 probability of being in an accident in a given year, while for a reckless driver the probability is 0.3. What is the probability that a randomly selected driver will have an accident within a year? (Enter your answer to two decimal places.)

1. Consider the following information on three stocks in four possible future states of the economy:                                                                                                (6 marks total)

a.   Your portfolio is invested 50% in A, 20% in B, and 30% in C. What is the expected return of your portfolio?                                                            

b.   What is the variance of this portfolio?                                                          

c.   What is the standard deviation of this portfolio?                               (1 mark)

How can I reduce data set by deleting any rows that have all FALSE bool values for every column in
that row using pandas. Assuming there are 20+ columns/rows to loop through. Example: The table data below the pandas code should drop/reduce the data to remove the second & fifth row. True and False in the table are dtype bool.

A perceptron with a unipolar step function has two inputs with weights w1= 0.5 and w2= -0.2, and a threshold theta=0.3 (theta can therefore be considered as a weight for an extra input which is always set to -1). The perceptron is trained using the learning rule ∆w = η (d − y) x, where x is the input vector, η is the learning rate, w is the weight vector, d is the desired output, and y is the actual output.What are the new values of the weights and threshold after one step of training with the input vector x = [0, 1]^T and desired output 1, using a learning rate η = 0.5?

Green Thumb Gardening is a small gardening service that uses activity-based costing to estimate costs for pricing and other purposes. The proprietor of the company believes that costs are driven primarily by the size of customer lawns, the size of customer garden beds, the distance to travel to customers, and the number of customers. In addition, the costs of maintaining garden beds depends on whether the beds are low maintenance beds (mainly ordinary trees and shrubs) or high maintenance beds (mainly flowers and exotic plants). Accordingly, the company uses the five activity cost pools listed below:

The company already has completed its first stage allocations of costs and has summarized its annual costs and activity as follows:

Required:

Compute the activity rate for each of the activity cost pools.

Green Thumb Gardening is a small gardening service that uses activity-based costing to estimate costs for pricing and other purposes. The proprietor of the company believes that costs are driven primarily by the size of customer lawns, the size of customer garden beds, the distance to travel to customers, and the number of customers. In addition, the costs of maintaining garden beds depends on whether the beds are low maintenance beds (mainly ordinary trees and shrubs) or high maintenance beds (mainly flowers and exotic plants). Accordingly, the company uses the five activity cost pools listed below:

The company already has completed its first stage allocations of costs and has summarized its annual costs and activity as follows: