Suppose X and Y are independent random variables and take values 1, 2, 3, and 4 with probabilities 0.1, 0.2, 0.3, and 0.4. Compute
(a) the probability mass function of X + Y
(b) E[X + Y ]?

Create an C# application named ConvertMilesToKilometers whose Main() method prompts a user for a number of miles, passes the value to a method that converts the value to kilometers, and then returns the value to the Main() method where it is displayed.

I need an equation for finding the veocity of water at the end of an incline.

• the velocity at the top is 0
• the incline is a right triangle with a hieght of 3000ft and a base of 9 miles
• the fluid is water
• the depth of the water is 3ft

1. A researcher wanted to estimate the mean contributions made to charitable causes by all major companies. A random sample of 18 companies produced by the following data on contributions (in millions of dollars) made by them.
1.8, 0.6, 1.2, 0.3, 2.6, 1.9, 3.4, 2.6, 0.2
2.4, 1.4, 2.5, 3.1, 0.9, 1.2, 2.0, 0.8, 1.1

Assume that the contributions made to charitable causes by all major companies have a normal distribution.
a. What is the point estimate for the population mean?
b. Construct a 98% confidence interval for the population mean.
c. What sample size would the researcher need to obtain a margin of error of 100,000 for the same confidence level? (Assume that the sample standard deviation obtained from his original sample is equal to the population standard deviation.)
d. Prior to collecting the data, the researcher believed that the mean contribution of all companies was less than $2.5 million. For a significance level of 0.01, test the researchers hypothesis.

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $15 million, it currently uses only common equity, it has no future plans to use preferred stock in its capital structure, and its federal-plus-state tax rate is 40%. The CFO has estimated next year's EBIT for three possible states of the world: $4.8 million with a 0.2 probability, $1.5 million with a 0.5 probability, and $0.8 million with a 0.3 probability. Calculate Neal's expected ROE, standard deviation, and coefficient of variation for each of the following debt-to-capital ratios. Do not round intermediate calculations. Round your answers to two decimal places at the end of the calculations.

~Debt/Capital ratio is 0.

~Debt/Capital ratio is 10%, interest rate is 9%.

~Debt/Capital ratio is 50%, interest rate is 11%.

~Debt/Capital ratio is 60%, interest rate is 14%.

The wind chill factor depends on wind speed and air temp. This data represents the wind speed (in miles per hour) and wind chill factor at an air temp. of 15 degrees F. Wind speed(x) 5, 10, 15, 20, 25, 30, 35 Wind chill(y) 12, -3, -11, -17, -22, -25, -27 Compute the least squares regression line and correlation coefficient for this data. Predict the wind chill for a wind speed of 50 miles per hour. Determine the wind speed (to the nearest mile per hour) for a wind chill of -45 degrees F. State the percentage of explained variation for the data set. State the value for the sum of the squared residuals.

Suppose that you want to estimate the number of miles driven per year among all drivers living in Vermont and how the number of miles driven is related to a driver’s age. Suppose that you obtain a list of all drivers licensed by the State of Vermont, then take a simple random sample of 1000 drivers from the list and ask them to complete a survey regarding their driving habits during the last year and their age. A total of 620 people complete the survey.

1. Identify the population, sampling frame, sample, and sample size.
2. List two ways that sampling bias may have been introduced.
3. Would you consider this to be a cross-sectional study or a longitudinal study? Explain your reasoning.

Suppose that you want to estimate the number of miles driven per year among all drivers living in Vermont and how the number of miles driven is related to a driver’s age. Suppose that you obtain a list of all drivers licensed by the State of Vermont, then take a simple random sample of 1000 drivers from the list and ask them to complete a survey regarding their driving habits during the last year and their age. A total of 620 people complete the survey.

1. Identify the population, sampling frame, sample, and sample size.
2. List two ways that sampling bias may have been introduced.
3. Would you consider this to be a cross-sectional study or a longitudinal study? Explain your reasoning.

1. Consider the following set of data relating Distance from School and Time to get to school:

1. Construct a scatter plot for the given data.

2. Does the scatter plot show positive/negative/no correlation? Justify your answer.

3. Find the least-square regression line (Best fit line).

4. If a student lives 6.8 miles away from school, what is her predicted time to get to school?

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e. Is there a linear correlation between the two variables? (Hint: find t-test statistic value)