For each of the following subproblems:i. Plot the distribution you’re sampling from (e.g., ifXi∼Exp(λ), plot the exponentialdistribution with rateλ). See Lab 3 for a reminder on how to do this.ii. Generate a sample of sizen= 10 from the distribution, and find the sample mean.iii. Repeat step ii. 999 times (i.e.,k= 1000), and then plot a histogram of the samples.iv. Add a plot of the approximate normal density on top of the histogram.v. Repeat steps ii. – iv. with sample sizen= 100.

(a)Xiiid∼Uniform(−2,2)

(b)Xiiid∼Gamma(k= 2,λ= 0.5)

(c)Xiiid∼Poisson(λ= 1)

(d)Xiiid∼Geometric(p= 0.2)

Consider the population of all 1-gallon cans of dusty rose paint manufactured by a particular paint company. Suppose that a normal distribution with mean μ = 4 ml and standard deviation σ = 0.2 ml is a reasonable model for the distribution of the variable x = amount of red dye in the paint mixture. Use the normal distribution model to calculate the following probabilities. (Round your answers to four decimal places.)

(a) P(x < 4) =  

(b) P(x < 4.2)=  

(c) P(x ≤ 4.2) =

(d) P(3.6 < x < 4.2) =  

(e) P(x > 3.5) =  

(f) P(x > 3) =

*PLEASE SHOW WORK. THANK YOU!

An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 15% and a standard deviation of return of 25%. Stock B has an expected return of 12% and a standard deviation of return of 20%. The correlation coefficient between the returns of A and B is 0.2. The risk-free rate of return is 1.5%.

A.)Approximately what is the proportion of the optimal risky portfolio that should be invested in Stock B?(HINT-0.636 IS NOT THE ANSWER-MARKET WRONG)

B.)What is the Expected Return on the Optimal Portfolio?

C.) What is the REWARD to VARIABILITY Ratio of the Optimal Portfolio?

Show where you input the numbers to follow the formula, thank you.

The question is to use Matlab to find the clamped cubic spline v(x) that interpolates a function f(x) that satisfies: f(0)=0, f(1)=0.5, f(2)=2, f(3)=1.5, f'(0)=0.2, f'(3)=-1 and then plot v(x).

This is my code so far:

x = [0 1 2 3];

y = [0 0.5 2 1.5];

cs = spline(x,[0 y 0]);

xx = linspace(0,3,101);

figure()

plot(x,y,'o',xx,ppval(cs,xx),'-');

IS THIS RIGHT? HOW CAN I GET MATLAB TO GIVE ME THE EQUATION OF v(x)?

1. For each of the following processes, a sample of size 500 is collected in order to estimate the process mean and variability. (30 points)

1. Indicate which measure of process capability (Cpvs.Cpk ) appears the more appropriate to use for each process and state why. (10 points)

For the Process A:

For the Process B:

2. Compute the appropriate measure of process capability for each process. (20 points)

Process A:

Process B:

4) A pediatrician wishes to recruit 4 couples, each of whom is expecting their first child, to participate in a new natural childbirth regimen. Let p = 0.2 represent the probability that a randomly selected couple agrees to participate.

a) What is the probability that 15 couples refuse to participate before 4 are found who agree to participate?

b) What is the probability that 12 couples refuse to participate before 4 are found who agree to participate?

c) What is the expected value of the total number of couples that must be asked to have 4 participating couples?

d) What is the variance of the total number of couples that must be asked to have 4 participating couples.

1.) the price elasticity of demand for margarine is -1.3 and the income elasticity of demand for margarine is -0.2.

a. Based on these figures, is the demand for margarine elastic or inelastic? How can you tell?

b. If the price of margarine falls by 5%, by what percentage will the quantity of margarine demanded change? Will it rise or fall?

c. If the price of margarine falls by 5%, by what percentage will the total revenue from sales of margarine (or total consumer spending on margarine) change? Will it rise or fall?

d. If consumer incomes rise by 10%, would the share of consumer income spent on margarine rise, or would it fall? Calculate an estimate of the percentage change in the share of income spent on margarine as a result of a 10% increase in income.

The constituents of a media for growing Hydrogenovibrio crunogenus are listed below.

     CONSTITUENTS                                                      ____                         AMOUNTS

      Sodium bicarbonate (NaHCO₃)                                                       5.0 grams

      Ammonium phosphate, monobasic [NH₄H₂PO₄]               1.0 gram

      Sodium chloride [NaCl]                                        5.0 grams

      Magnesium sulfate [MgSO₄ . 7H₂O]                            0.2 gram

      Potassium phosphate, dibasic [K₂HPO₄]                                  1.0 gram

      Iron III carbonate [Fe₂(CO_­3)₃]                                                          5.0 grams        

      Water [H₂O]                                                                                       982.8 grams                            

1. What type of microorganism is Hydrogenovibrio crunogenus based on the ingredients of this media-photoheterotroph, chemoautotroph,    chemoheterotroph, or photoautotroph?

2. What are the sources of nitrogen and phosphorus in this media?

3. Is the media chemically-defined or complex?

4. Is the media a liquid or semi-solid?

Fluid Mechanics Friction Problem: Write one MATLAB m-file that solves the Type I and II problems presented in class based on the file posted for the Type III problem (use Colebrook to estimate f). Type I: Solve hL for v=0.74x10-5ft^2/s, D=3 in, L=1000 ft, e=0.006 in, and Re=80000. f=0.0258 from Moody Chart. Type II: Solve Q for v=10^-6 m^2/s, D=0.2 m, L=500 m, e=0.046 mm, and hL=30m. Use “rough” Colebrook to generate an estimate for f.