Please explain and show work.

Joseph’s utility function is given by UJ = xA + 2xB, where xA denotes his consumption of apples and xB his consumption of bananas. Clara’s utility function is given by UC = 3xA + 2xB. Joseph and Clara shop at the same grocery store.

a. When we observe that Joseph leaves the store with some bananas, then we can deduce that Clara also buys some bananas.

b. There exist prices of apples and bananas such that both consumers buy strictly positive amounts of both goods.

c. When we observe that Joseph leaves the store with some apples and some bananas, then we can deduce that Clara also buys some apples and some bananas.

d. When we observe that Joseph leaves the store with some apples, then we can deduce that Clara also buys some apples.

e. Apples and bananas are perfect complements for Joseph.

An experiment consists of flipping a coin 5 times and noting the number of times that a heads is flipped. Find the sample space SS of this experiment.

Design an experiment that would resolve the nature versus nurture controversy. What are some reasons why this experiment hasn’t been done?

How is the discrete choice experiment method different from the contingent valuation method?

What are some relative advantages of the discrete choice experiment method as compared to the contingent valuation method?

Can you think of any examples where the contingent valuation method may be more practical than the discrete choice experiment method?

EXPLAIN WHY.

(a) Find ​P(T<1.321) when v=22. ​(b) Find ​P(T>2.069​) when v=23. ​(c) Find ​P(−2.145<T<2.997​) when v=14. ​(d) Find ​P(T>−2.998) when v=7.

describe an experiment that would test whether the saying "Honesty is the best policy" is true or not. The description of your experiment should include:

- the design of your study (how many groups; how are they different)

- the independent and dependent variables

- how you are operationally defining the constructs (how you will measure or manipulate the constructs)

Note that it should be an experiment, not a correlational study or other method.

discuss the importance of using a scientific experiment to answer if this belief is true. Make sure to discuss why the scientific approach is better than using personal anecdotes for this specific belief.

the experiment you undertook to test one of the factors that affects diffusion of a solute in a solvent: Parameter chosen: Null hypothesis: Alternate hypothesis: Dependent variable: Independent variable: Controlled variables: Write a detailed protocol on how you would perform the experiment and measure the results. You can use dot points to detail the steps taken to perform the experiment – make sure you mention all details of the materials you use so that anyone reading these instructions could repeat the experiment and would get the same results. Experimental protocol

145&146&147. The potential of a silver electrode is measured relative to an Ag-AgCl electrode for the titration of 100.0 mL of 0.100 M Cl with 0.100 M Ag+. What is the potential after 75.00 mL of titrant is added. Eo = 0.799 V for Ag+, E = 0.197 V for the Ag-AgCl electrode and Ksp = 1.8 × 10−10.

A) 0.493 V

B) 1.070 V

C) 0.521 V

Specify sample spaces for the random experiments (a)-(e) and give mathematical descriptions of the corresponding events. (a) Experiment: A coin is tossed three times. Event: The result of the second toss is “heads”. (b) Experiment: Three indistinguishable coins are tossed at the same time. Event: At most two of the coins show “heads”. (c) Experiment: A die is rolled until each number has appeared at least once. The outcome is the number of rolls needed. Event: Less than 15 rolls are needed. (d) Experiment: n devices labeled with 1, . . . , n are inspected. It is of interest which devices are working and which are not. Event: The first three devices are defective. (e) Experiment: n devices are inspected. Interest lies in the number of defective devices. Event: Exactly three devices are defective.