a) Consider an ideal gas in a container with a frictionless piston. The gas is isothermally compressed at 26 degrees

Celsius as 940 Joules of work is done on it. Determine the resulting change in entropy of the gas, the change in entropy

of the environment and the universe. (assume the temperature of the environment is a constant 22 Celsius)

b) 20 grams of ice at 0 Celsius melt while being left at room temperature of 22 Celsius. After melting, its temperature

rises to 22 Celsius. Determine the resulting change in entropy of the gas, the change in entropy of the environment and

the universe.

c) If you are rolling a pair of dice, what is the entropy of the mactrostate 2, macrostate 5, and macrostate 7? Imagine a

pair of dice starts with a macrostate of 2 and then you roll it 5 times and get the following results: 5, 9, 7, 3, 8. What is

the resulting change of the entropy of the universe for each roll and for all 5 rolls put together?

Answers should be:

a) ΔSgas = -3.14 Joule/K, ΔSenvironment = +3.18 Joule/K, ΔSuniverse = +.04 Joule/K

b) ΔSice = +30.9 Joule/K, ΔSenvironment = -28.8 Joule/K, ΔSuniverse = +2.1 Joule/K

c) S2 = 0, S5 = kln4, S7 = kln6

ΔS1 = kln4, ΔS2 = 0, ΔS3 = kln(1.5), ΔS4 = -kln3, ΔS5 = kln(2.5), ΔStot = kln5

1. Determine if the following statements are correct and then explain briefly.

a. Policymakers in a closed economy could promote economic growth by encouraging saving.

b. When the government removes the minimum wage law, natural unemployment will fall.

c. If inflation is lower than expected, creditors gain at the expense of debtors.

d. Increase unemployment benefit payment to the unemployed will increase unemployment.

Suppose that an automobile has a painted surface area of 270 ft2 . After a decade of use, the number of scratches on this automobile follows a Poisson distribution, with a rate of λ = 0.025 scratch/ft2 .

(a) Compute the mean and variance of the number of scratches on the car after a decade of use.

(b) Compute the probability that the entire car has at most four scratches after a decade of use.

(c) Compute the probability that the entire car has more than seven scratches after a decade of use.

Suppose that an automobile has a painted surface area of 270 ft2 . After a decade of use, the number of scratches on this automobile follows a Poisson distribution, with a rate of λ = 0.025 scratch/ft2 .

(a) Compute the mean and variance of the number of scratches on the car after a decade of use.

(b) Compute the probability that the entire car has at most four scratches after a decade of use.

(c) Compute the probability that the entire car has more than seven scratches after a decade of use.

DATA SET: 105, 82, 94.5, 72.5, 92, 91, 52, 86, 100, 96, 98, 109, 96, 103, 68

Q1. What is the 15% trimmed mean of these 15 data points?

Q2. What is the sample mean of these 15 data points?

Q3. What is the probability that a randomly chosen number among these data points is between 95 and 100, exclusive of the ends?

Q4. What is the probability that a randomly chosen number among these date pints is not a multiple of 5?

8. Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Suppose that 650 couples each have a baby; find the mean and standard deviation for the number of girls in the 650 babies.

9.A sales firm receives an average of four calls per hour on its toll-free number. For any given hour, find the probability that it will receive exactly five calls. Use the Poisson distribution.

The first row of the table below shows the number of individuals of each of three genotypes in a given population in the summer of 2015.

The second row shows the relative probability that each of these genotypes survives over the winter (the relative fitness based on survival).

If you resurvey the population in the spring of 2016, how many SS individuals would you expect to find?

They have available 10 boxes of honey, 4 boxes of el Duende, 6 boxes of bimbos, 15 boxes of oreos . Each sells for 6$.

a) Define your random variable.

b) Determine the probability distribution and parameters for the random variable.

c)Suppose that, after two hours, ten boxes of them have been purchased. Determine the cumulative distribution function for the number of honey purchased.

d)Draw the probability distribution function for the number of honey purchased.

Some body please hurry

An internet search engine looks for a certain keyword in a sequence of independent websites. It is believed that 35% of the sites contain this keyword.

(a) Let X be the number of websites visited until the first keyword is found. Compute the probability that the search engine had to visit at least 10 sites in order to find the first occurrence of the keyword.

(b) Out of the first 25 websites, let Y be the number of sites that contain the keyword. Compute the probability that at least 10 of the first 25 websites contain the keyword.