The volume of a cylinder is V space equals space pi space r squared space h, where r is the radius of the circular faces and h is the height of the cylinder. Your measurements show that the mean value of r is 21 cm and its statistical and instrumental uncertainties turned out to be 0.10 cm and 0.20 cm, respectively. Likewise, that of h are 13 cm for the mean, 0.2 cm (statistical) and 0.3 cm (instrumental) for its uncertainties. What can you say about which source of uncertainty has the largest contribution to the overall uncertainty of V ? What would you need to do to improve (reduce) the uncertainty on your calculation of V?

Refer below table on the average prices, how to make a decision on KL or Penang residential prices are higher than other Peninsular states? Explain in detail.

An investor purchased 550 shares of stock A at $22.50 per share and 1,050 shares of stock B at $30.50 per share one year ago. Stock A and stock B paid quarterly dividends of $2.50 per share and $2.00 per share, respectively, during the year. One year later, the investor sold both stocks at $30.50 per share. The correlation coefficient (ρ_AB) is 0.3 and the standard deviations of stock A and stock B are 20.5 percent and 15.5 percent, respectively.

Calculate the standard deviation of the portfolio. (Round intermediate calculations to 4 decimal places, e.g. 15.2512 and the final answer to 2 decimal places, e.g. 15.25%.)

Consider the following stock information about Tencent and HSBC

a. What’re the expected return on each stock?
b. What’re the standard deviation on each stock?
c. The risk free rate is 1.5%. Based on the CAPM, If Tencent’s market beta is 1.5, what’s the beta of HSBC?
d. If you invested 65 percent in Tencent and 35 percent in HSBC, what is your portfolio expected return? The standard deviation?
e. Given the portfolio information in (d) and beta information in (c), what is the portfolio’s market beta?

1. A stock portfolio has an expected return of 12% and a standard deviation of 20%. A bond portfolio has an expected return of 6% and a standard deviation of 9%. The two portfolios have a correlation coefficient of 0.3. T-Bills have an expected return of 2%. Your coefficient of risk aversion is 7. (15 points)

1. What are the weights of the minimum variance portfolio that can be formed between the two portfolios if they are the only risky assets being considered?

2. What is the expected return and standard deviation of the minimum variance portfolio?

3. How much should you allocate between T-Bills and the risky portfolio?

4. What is the expected return and standard deviation of your complete portfolio?

use r programming, details on the codes please.

Consider an urn with 10 balls inside, 7 of which are red and 3 of which are green. Select 3 balls successively from the urn. Let A = {1 st ball is red}, B = {2 nd ball is red}, and C = {3 rd ball is red}. Then P(all 3 balls are red) = P(A ∩ B ∩ C)

     a) Calculate the Probability with R? (1)

     b) Also, what is the probability of observing red, then green, then red? (1)

Let us roll a 4-sided die three times. a)Let us define the random variable U = X1 − X2 + X3. What is the probability that U > 6. (1) b) Also, if A = X1+X2+X3, What is the probability of A > 9.(1)

3. Randomized Controlled Trials are a type of medical experiment, where the eligible participants are randomly assigned (allocated) to one of the two (or more) branches of the study. A randomized controlled trial is considered the gold standard of clinical trials. In these studies, randomization helps to control for confounding factors, and evenly distribute prognostic factors across groups. This is somewhat like a loaded dice experiment.

            Let’s create an “unfair” dice that has a 0.35 probability of resulting in a 6, and a    probability of 0.13 for each of the other outcome.

Hint: Use the sample command.

a) Simulate a sample of 10 trials of throwing the dice. (1)

b) How many 6’s do you get count using R. (1)

Write a function cancerservival where the probability of cure, recurrence, metastasis and death are (0.3, 0.3, 0.25 and 0.15 respectively). (2)
a) Use the function to simulate the results of 100 cancer occurrences. (1)

b) Report the number of patients cured. (1)

A second-hand car dealer is doing a promotion of a certain model of used truck. Due to differences in the care with which the owners used their cars, there are four possible quality levels (q1 > q2 > q3 > q4) of the trucks on sale. Suppose that the dealer knows the car’s quality (quite obvious), but buyers only know that cars for sale can be of quality q1, q2, q3 or q4. Faced with a given car, the buyers cannot identify its precise quality. However, they believe that there is a probability 0.2 that the quality is q1, a probability 0.3 that it is q2, and a probability 0.3 that it is q3. The respective values of the cars to the buyers are $20,000 for the q1 quality, $15,000 for q2, $10,000 for q3 and $5,000 for q4.

Assume that all agents (including the buyers) are risk neutral (only care about “return”) in the sense that a buyer does not want to pay more for a car than its expected worth and the car owner (the car dealer) does not wish to sell at less than what the car is worth.

a) Define adverse selection in general and in the current context.

b) If all four types of used truck are offered for sale, what is the highest price a buyer would be willing to pay for a used truck? At this price, what type(s) of truck will be offered for sale?

c) Now suppose the $20,000 trucks are no longer offered for sale but other types are (and is known to the buyers). What is the maximum price a buyer is willing to pay for a used truck? At this price, what type(s) of truck will be offered for sale? [Hint: What are the respective probabilities of the types of cars that will be offered for sale?]

d) Explain how adverse selection causes this market to a partial market breakdown (i.e., only the worst used trucks (q4 type) are traded in the market).

Question 3: Please create a statement of cash flow with indirect method- Please provide answers to each category and a one paragraph analysis of the cash flow using the indirect method.

Statement of Cash Flow with Indirect method

Instructions:You need to show your clear calculation to support each statement provide a paragraph of interpretation related to the result of your analysis on each statement.

Comparative Analysis for balance sheet:

Researcher conducts a study to decide whether support groups improve academic performance for at-risk high school students. Ten such students are randomly selected to take part in the support group for a semester, while the other 10 at-risk students serve as a control group. At the end of the semester, the improvement in GPA versus the previous semester is recorded for each student.
Support Group: 0.5, 0.8, 0.7, 0.7, -0.1, 0.2, 0.4, 0.4, 0.5, 0.4
Control Group: -0.3, 0.0, -0.1, 0.2, -0.1, -0.2, -0.2, 0.0, -0.1, 0.1

At the 10% level, use R to compare the two groups using a permutation test (with 100,000 randomly generated permutations). You need to write your hypotheses, the test statistic, the pvalue, and the decision/conclusion in the context of the problem.

R code for reference:

SupportGroup <- c(0.5, 0.8, 0.7, 0.7, -0.1, 0.2, 0.4, 0.4, 0.5, 0.4)
ControlGroup <- c(-0.3, 0.0, -0.1, 0.2, -0.1, -0.2, -0.2, 0.0, -0.1, 0.1)

mean(SupportGroup);sd(SupportGroup)
mean(ControlGroup);sd(ControlGroup)

#permutation test on difference of means
choose(20,10)#number of possible permutations
new.dat <- c(SupportGroup,ControlGroup)
obs.mean.diff <- mean(SupportGroup) - mean(ControlGroup)
nsim <- 100000
sim.mean.diff <- rep(NA,length=nsim)
for (i in 1:nsim){
grps <- sample(c(rep(1,10),rep(2,10)),replace=FALSE)
sim.mean.diff[i] <- mean(new.dat[grps==1]) - mean(new.dat[grps==2])
}

hist(sim.mean.diff);abline(v=obs.mean.diff,col="red",lty=2)
length(sim.mean.diff[sim.mean.diff<=obs.mean.diff])/nsim #estimated p-value