1. You are given the following payoff table with profits (in $).

Assume the following probability information is given, where I1 and I2 are the outcomes of the sample information available:

1. [2] Find the values of P(I1) and P(I2).

2. [2] Determine the values of P(s1 | I1), P(s2 | I1), P(s1 | I2), and P(s2 | I2).

[4] Determine the optimal strategy based on the sample information I1 and I2. What is the expected value of your solution?

1. A recruiter, Joey Falcon, interviews 6 students. Each student has a probability of 0.2 of receiving a recommendation from Joey Falcon (the result from each student is independent from the results of the other students). Let X be the number students who Joey Falcon recommends.

A second recruiter, Sophie Secaucus, interviews 4 students (different from the above 6 students). Each student has a probability of 0.3 of receiving a recommendation from Sophie Secaucus (the result from each student is independent from the results of the other students. Let Y be the number of students who Sophie Secaucus recommends.

1. Find the joint pmf for X,Y (assume X and Y are independent).
2. Find p(X<3, Y<2)
3. Find p(X+Y<5)

The flow rate of warm air into the air conditioning is 5,000 cfm. An air conditioning system takes outdoor air at 95 degrees F dry-bulb and 70% relative humidity, and discharges it at 60 degrees F dry-bulb and 95% relative humidity. The air conditioning system operates on a vapor compression cycle using R134a between 20 and 200 psia. Refrigerant enters the compressor at 20 degrees F and leaves the compressor at 180 degrees F. Refrigerant enters the evaporator coil at a quality of x = 0.3. Determine a) The quantity of water removed from the air, in lb/min. b) The quantity of heat removed from the air, in tons. c) The mass flow rate of refrigerant, in lb/s. d) The compressor's power requirement, in hp.

You are an industrial chemist working for a company that makes methanol (CH3OH) according to the equilibrium reaction shown below. You love your job, except that your assistant does not have the best notebook keeping skills. One day you set up the reaction with the equilibrium concentrations shown below.

CO (g) + 2 H2 (g) <--> CH3OH (g) 0.24 M 1.1 M 0.15 M at 327oC

Later on your assistant mentions that he added some more CO, but he doesn't remember how much. But he also remembers that as the equilibrium was being reestablished, the hydrogen concentration changed by 0.3 M, although he doesn't remember if it went up by that much, or down by that much. How much carbon monoxide did he add, in M?

1. In the following regression, “drive” is a dummy indicating a person owns a personal vehicle, “employed” is a dummy indicating a person is employed, “age” is a person’s age, and “married” is a dummy indicating a person is married:

drive=0.3+0.2 employed+0.003 age+0.4 married

The command in STATA is: reg drive employed age married

1. Interpret the coefficient 0.2 on employed.  

2. Predict the probability of owning a vehicle for a person who is employed, 60 years of age and married.  

Drive=.3+.2(1)+.003(60)+.4(1)=1.08

3. The answer you got from the previous question is actually greater than 1. Explain why that is.  

Will you be able to test the significance of the coefficients if you were given all the standard errors and/or p-values? Say “yes” or ‘no”, then explain.

1. Joe estimated the heritability of conception rate in his heifers and it was much higher than he expected at 0.25. Joe’s brother estimated the heritability of conception rate at his farm and it was much lower at 0.03. Both brothers knew that heritability varied by population but they still didn’t understand why there values were so different. What could have Joe don at his ranch to increase the heritability over the estimated heritability of his brother? (3 pts)

2. If Jan was raising ducks,

(a) What is the repeatability of the number of goslings hatched in a nest if the phenotypic variance was 0.3 and the producing ability variance was 0.2? (1 pt)

(b) If the average number of goslings hatched in a nest was 6 and Jan’s goose had 8 goslings in her nest, what would her producing ability be? (1 pt)

You are planning a study of attitudes to the length of jail sentences for homicide, using a scale running from –4 to +4, where 0 indicates a judgment that current sentences are about right. Previous research suggests that the population SD for the scale is 1.2. You plan to use a single sample and would like to be able to detect a true effect of 0.5 scale units, using α = .01. If you use N = 100, using the same scale to compare attitudes in two very different neighborhoods. You would like to be able to detect a difference of 0.3 scale units. Consider power and make recommendations.

This is an exercise problem in one of the textbook by Geoff Cummings, Understanding The New Statistics, this is the first problem of chapter 12. This is all the information that it has and I must come with an answer regarding power and recommendations.

Problem: Using the alternative-parameter method, determine the parameters of the following distributions based on the given assessments.

Find the parameter value β for the exponential distribution given:

P_E (T ≤ 15 \ β) = 0.50.

Find the parameters μ and s for a normal distribution given:

P_N (Y ≤ 25\ μ, s) = 0.25 and P_N (Y ≤ 125\ μ, s) = 0.75

Find the Min, Most Likely, and Max for the triangular distribution given:

P_T (Y ≤ 15\Min, Most Likely, Max) = 0.15

P_T (Y ≤ 50\Min, Most Likely, Max) = 0.50, and

P_T (Y > 95\Min, Most Likely, Max) = 0.05

Find the parameters values a₁ and a₂ for the beta distribution given:

P_B (Q ≤ 0.3\a_1, a₂) ₌ 0.05 and P_B (Q ≤ 0.5\a_1, a₂) ₌ 0.25

Basic calculations based on the Central Limit theorem: Determine the appropriate ^µ_X and σ_X given the population mean is 1020, σ is 153, and with a normal x-distribution, if Basic calculations based on the Central Limit theorem: Determine the appropriate ^µ_X and σ_X given the population mean is 1020, σ is 153, and with a normal x-distribution, if

a) n=16

b) n=50

c) n=1000

8) Determine the following probabilities given a normal x-distribution(convert to z first):

(a) µ is 8, σ is 17 with n = 64. Find P(_X>9).

(b) µ is 20, σ is 3 with an n = 36. Find P(_X<19).

(c) µ is 32, σ is 0.3 with an n = 20. Find P(31.8<_X<31.9).