Packets arrive at an infinite buffer at a Poisson rate of 100 packets/sec, and are transmitted over a link of rate 1 Mbps in an FCFS manner. An arriving packet is a 100-bit packet with probability 0.2, a 1000-bit packet with probability 0.5, and a 10000-bit packet with probability 0.3 . Find (a) the average waiting time for a packet, and (b) the average number of packets in the buffer, in steady state.

Chlorophyll is known to have its absorption maximum at 680 nm (red light) with the extinction coefficient of 105 L/mol*cm. Assume a plant with leaves about 0.6 mm thick with the chlorophyll concentration of 0.0005 mol/L. How much red light in [%] will pass through a typical leave? Select one: a. 0.1 b. 10 c. 0.01 d. 0.3 e. 1

Consider the same football situation as in the previous question, but now suppose the payoffs (probabilities of winning) are as given in the following normal form:

Do any of the teams (the one playing defense or the one playing offense) has a dominant strategy? Which one? Explain why.

Suppose that the USDA expects that 53.3 billion bushels of soybeans will be produced this year at a price of $8.50/bushel. Assume that the elasticity of supply is 0.3 and that the elasticity of demand is -0.2 (both very inelastic).

2. What quota is required to increase the soybean price to $9.25/bushel? And what is the economic cost of this solution (i.e., what is the change in producer surplus and change in consumer surplus, and what is the sum of these changes)?

A European at-the-money call option on a currency has four years until maturity. The exchange rate volatility is 10%, the domestic risk-free rate is 2% and the foreign risk-free rate is 5%. The current exchange rate is 1.2000. What is the value of the option?

0.98N(0.25)-1.11N(0.05)

0.98N(-0.3)-1.11N(-0.5)

0.98N(-0.5)-1.11N(-0.7)

0.98N(0.10)-1.11N(0.06)

A day’s production of 850 parts contains 50 defective parts. Three parts are selected at random without replacement. Let the random variable ? equal the number of defective parts in the sample.

1. Find the probability mass function

2. Find the cumulative distribution function of ?.

3. Find ?(? > 0.5) =

4. Find ?(1.5) =

5. Find ?(2) − ?(0.3) =

6. Find ?(0.99 < ? < 2.5) =

6. BSA has the following amino acid profile compared with the average of known vertebrate proteins:

Based upon this data, is BSA a good standard to use in the Bradford assay? Explain your answer.

Suppose that the chance of rain tomorrow depends on previous weather conditions only through whether or not it is raining today and not on past weather conditions. Suppose also that if it rains today, then it will rain tomorrow with probability 0.6, and if it does not rain today, then it will rain tomorrow with probability 0.3, then

a. Calculate the probability that it will rain four days from today given that it is raining today.

b. What is the limiting probability of rain.