Χ if 0 < x ≤ 45 1350 f(x) = 60-x if 45 < x ≤ 60 450 0
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DHL usually gives its customer a 60-minute window in which it expects home deliveries to be delivered. An independent consultant estimates that the final delivery time within the window is a delivery that follows the following condensation
a. Draw the density function of the
b. What is the
c. What is the variance of the event?
![Χ
if 0 < x ≤ 45
1350
f(x) =
60-x
if 45 < x ≤ 60
450
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- Consider the rate of return of stocks ABC and XYZ. Year rABC rXYZ 1 22 % 34 % 2 12 12 3 14 18 4 7 0 5 1 −8 a. Calculate the arithmetic average return on these stocks over the sample period. b. Which stock has greater dispersion around the mean return? A. XYZ C. ABC c. Calculate the geometric average returns of each stock. What do you conclude? (Do not round intermediate calculations. Round your answers to 2 decimal places.) d. If you were equally likely to earn a return of 22%, 12%, 14%, 7%, or 1%, in each year (these are the five annual returns for stock ABC), what would be your expected rate of return? (Do not round intermediate calculations.) e. What if the five possible outcomes were those of stock XYZ? f. Given your answers to (d) and (e), which measure of average return, arithmetic or geometric, appears more useful for predicting future performance? A. Arithmetic B. Geometric4. When the Titanic sank in 1912, there were over 1,300 passengers aboard. A random sample of 50 passengers that were aboard is taken. The amount they paid for the voyage and whether or not they survived is recorded. A model is fit to predict the probability they survived when the ship sank is obtained. Survived Logistic Fit of Survived By Fare 1.00 0.75 0.50- 0.25- 50 4 Parameter Estimates 100 Term Intercept -1.404254 0.4353289 Fare 0.01246686 0.0097945 For log odds of Yes/No Fare Estimate Std Error ChiSquare 10.41 1.62 150 200 Prob> ChiSq 0.0013 0.2031 No Yes a) Suppose someone paid a fare of 25 pounds. Predict the probability they survived. b) How much would someone pay to have at least a 65% chance of survival?In a random sample of sixteen different industries the percentage employment x in STEM (science, technology, engineering, mathematics) and mean annual compensation y(in thousands of dollars) were recorded, with the following results. The scatter diagram showed a linear trend. SSxx = 1303.9 SSy= 1503.0 SSy = 2660.2 Ex = 150 .1 Ey = 915 n= 16 %3D %3D 1sxs 34 36.7 s y s 90.5 Calculate the linear correlation coefficient for percent employment in STEM and annual compensation and enter your answer below accurate to two decimal places.
- As concrete cures, it gains strength. The following data represent the 7-day and 28-day strength in pounds per square inch (psi) of a certain type of concrete. Complete parts (a) through (f) below. 7-Day Strength (psi), x 28-Day Strength (psi), y 4120 4620 2480 2890 3340 3380 2620 4630 5020 4190 (d) A normal probability plot suggests that the residuals are normally distributed. Test whether a linear relation exists between 7-day strength and 28-day strength at the a = 0.05 level of significance. State the null and alternative hypotheses. Choose the correct answer below. O A. Ho: Po =0 H1: Po #0 O B. H,: Po = 0 H1: Bo >0 OC. Ho: B, = 0 H;: B, #0 O D. Ho: B, = 0 H1: B, >0 Determine the P-value of this hypothesis test. P-value = (Round to three decimal places as needed.) What is the conclusion that can be drawn? O A. Reject H, and conclude that a linear relation does not exist between the 7-day and 28-day strength of a certain type of concrete at the a = 0.05 level of significance. O B.…Which of the following is a true statement? A. The expected value is the most frequently occurring value of the random variable. B. Variance is always >=0 C. Variance can be negative D. F(x)=P(X=x)A surgery has a success rate of 90%. Suppose that the surgery is performed on threepatients Graph the probability distribution for X using a histogram.Find the mean of X.Find the variance and standard deviation of X.
- Storm damage can occur to homes in any given year, with the amount of damage varying randomly from year to year. Let X represent the dollar value of storm damage in a given year. It is known that in 95% of the years, X = $0, while in 5% of the years, X = $20,000. What is the expected value and standard deviation of the damage in any given year?Consider the bivariate distribution for the random variables x and y. The correlation coefficient of x and y is the covariance a. Consider the bivariate distribution for the random variables x and y. The correlation coefficient of x and y is the covariance b. multiplied by the product of the standard deviations for x and y. c. multiplied by the standard deviation of y and divided by the standard deviation of x. d. multiplied by the standard deviation of x and divided by the standard deviation of y.Using the unemployment data provided, investigate the association between the male unemployment rate in 2007 and 2010 for a sample of 52 countries. Complete parts (a) through (4). m Click the icon to view the data table. OC The plot of the residuals against x tends to cluster as x increases, which is a possible violation of the Linearity Conditon. The Normal probability plot indicates that the Normal Population Assumption is satisfied. OD. The plot of the residuals againat x shows no patten, which satisfes the conditions for linear regression. The Normal probability plot indicates that the Nomal Probability Assumption is violated. c) Test an appropriate hypothesis using a- 0,05 to determine it the association is signiftcant. Choose the corect nul and altemative hypotheses. OA Ha: 0 OB. Ho: lo " 0 HA P0 or l 0 O C. Ho Po-0 OD. Ho: la =P HA Po
- EXERCISE 3.6 Winter lasts from December 21 through March 21. The average win- ter temperature in Boston is Normally distributed with mean μ = 32.5° F and stan- dard deviation o = 1.59° F. In New York City, the average winter temperature is Normally distributed with mean = 35.4 ° F and standard deviation o = 2.05°F. (a) What is the probability that the average winter temperature in Boston this com- ing winter will be above freezing (32 ° F)? (b) Assume that average winter temperatures in Boston and New York are inde- pendent. What is the probability that the average temperature in Boston in the coming winter will be higher than in New York? (c) Do you think the independence assumption above is reasonable? EXERCISE FIThe owner of a farmer's market was interested in determining how many oranges a person buys when they buy oranges. He asked the cashiers over a weekend to count how many oranges a person bought when they bought oranges and record this number analysis at a later time. The data is given below in the table. The random variable x represents the number of oranges purchased and P(x) represents the probability that a customer will buy x oranges. Determine the variance of the number of oranges purchased by a customer. Round to two decimal places. X P(x) 1 0.05 O A. 0.56 OB. 3.97 OC. 3.57 OD. 1.95 2 3 0.19 0.20 4 5 0.25 0.12 6 0.10 7 8 0 0.08 9 10- 0 0.01Below are data on economic condition, probability, and expected return on stock and bond funds in a year. Scenario Probability Stock Fund (%) Bond Fund (%) Severe recession 0.05 -37 -10 Mild recession 0.25 -11 10 Normal growth 0.40 14 7 Boom 0.30 30 2 Calculate expected return and standard deviation of each fund. Calculate covariance and correlation coefficient between stock fund and bond fund. Your portfolio is composed of 85% in bond fund and 15% in stock fund. Using Excel, calculate expected return and standard deviation of your portfolio based on Equations in the attached images. Discuss important implications with respect to portfolio theory as you evaluate all numbers in part a, b, and c above.
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