For this project:

Create a game with at least 3 outcomes

Develop a probability table with the outcomes for X and the probability p(X)

Find the expected value and standard deviation

Determine if your game is fair

How could be changed to make it fair or favor the player or "house"?

Run the game 50 times and record each outcome

Compute the empirical probability and compare it against the theoretical probability in #2. Find the average outcome of the 50 trials, and compare against the expected value

Please help ! I am confused with this project.

Discuss Briefly:

(a) The more debt a firm issues, the higher interest rate it must pay; thus firms should operate at conservative debt levels.

(b) Given the choice between two investment projects with the same systematic risk and the same expected return, all bondholders would prefer the project with the lower variance and all stockholders would prefer the project with the higher variance.

(c) Black-Sholes is inappropriate for valuing a levered firm’s equity, the empirical evidence indicates that higher interest rates are associated with lower stock prices.

1) Suppose X1,X2,...,Xn are iid Gamma(α,λ) random variables.

a) Express the first and third moments (µ1 = E(X) and µ3 = E(X3)) as functions of λ and α.

b) Solve this system of equations to find estimators of ˆ λ and ˆ α as functions of the empirical moments. Note that the estimates must be positive.

2) Suppose that X1,X2,...,Xn are a iid Beta(a, a) random variables. That is, a beta distribution with the restriction that b = a. Using the formulae for the expectation and/or variance, find a method of moments estimator for a.

An organic compound containing C, H, O, and S is subjected to two analytical procedures. In the first procedure a 9.33 mg sample is burned which gives 19.50 mg of C02 and 3.99 mg of H20. In the second procedure, a separate 11.05 mg sample is fused (melted) with Na202 and the resulting sulfate is precipitated as BaS04, which (when washed and dried) weighs 20.4 mg. (Appropriate amounts of Na202 and a compound containing barium ion are added.) The amount of oxygen in the original sample is obtained by difference. Determine the empirical formula of this compound.

A scientist is studying a monoprotic carboxylic acid that consists of only carbon, hydrogen, and oxygen. From a titration he finds that 13.4 mL of a 0.250 M sodium hydroxide solution are required to neutralize 0.5303 grams of the carboxylic acid. From a combustion experiment he finds that 2.982 grams of the carboxylic acid yields 0.9835 grams of carbon dioxide and 4.80 grams of water.

(a).What is the molecular weight of the carboxylic acid? g/mol

(b.)What is the empirical formula of the carboxylic acid?

(c.) What is the molecular formula of the carboxylic acid?

1- Write a function f(n,a,b) that generates n random numbers
# from Uniform(a,b) distribution and returns their minimum.
# Execute the function with n=100, a=1, b=9.

2- Replicate the function call f(100,1,9) 100 thousand times
# and plot the empirical density of the minimum of 100 indep. Unif(1,9)'s

3-Use the sampling distribution from (b) to find 95% confidence
# interval for the minimum of 100 independent Unif(1,9)'s.

Please solve in R

A specific chemical reaction to break down a compound follows a normal distribution with a mean time of 160 seconds and a standard deviation of 4 seconds.

(a)

What reaction time would result in a z-score of −1.5?

(b)

Using the Empirical Rule, what reaction time would have 84% of all values fall below it?

(c)

A reaction time that is shorter than 150 seconds or longer than 172 seconds will be re-run for quality control purposes. What is the probability that a reaction will need to be re-run?

The body temperatures of a group of healthy adults have a​ bell-shaped distribution with a mean of

98.13 degrees°F

and a standard deviation of

0.53 degrees°F.

Using the empirical​ rule, find each approximate percentage below.

Modern microeconomics, specifically consumer theory, is based on utility theory—consumers maximize their utility.

Where does our modern conception of utility theory come from? (Hint: there are multiple sources.)

What is the empirical basis for utility theory?

Can utility theory be considered scientific according to Karl Popper’s conception of science?

How about Kuhn or Lakatos?

What are the criticisms of utility theory and how would its supporters (e.g., Gary Becker) respond?

Are there any alternative paradigms? What are the flaws/limitations in these approaches?

Compound X, isolated from lanolin (sheep's wool fat), has the pungent aroma of dirty sweatsocks. A careful analysis showed that compound X contains 62% carbon and 10.4% hydrogen. No nitrogen or halogen was found.

a. Compute an empirical formula for compound X.

Express your answer as a condensed structural formula.

b. A molecular weight determination showed that compound X has a molecular weight of approximately 117. Find the molecular formula of compound X.

Express your answer as a condensed structural formula.