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1. Given a random variable X that has a t(ν) distribution, determine the value of x0 such that P (|X| x0) = 0.025 for (i) ν = 5; (ii) (i) ν = 25; (iii) ν = 50; (iv) ν = 100. Compare your results with the single value of x0 such that P (|X| x0) = 0.025 for a standard normal random variable X.
2. Plot on the same graph the pdfs for a Cauchy C(5, 4) random variable and for a Gaussian N (5, 4) random variable. Compute the probability P (X ≥ μ + 1.96σ) for each random variable, where, for the Gaussian random variable, μ and σ are the mean and standard deviation (positive square root of the variance) respectively; for the Cauchy distribution, μ and σ are, the location and scale parameters, respectively.
You own a small tea company, Sweet Leaf, NASDQ ticker symbol LEAF. You are looking at marketing costs versus benefits. Your production manager says it doesn't matter which tea you produce
List 4 variables that you might assess in a research project related to your research area. List one for each type of measurement scale: Nominal, ordinal, interval, and ratio
a popular flashlight that uses two d-size batteries was selected and several of the same models were purchased to test
Construct a payoff table for Mountain Ski's decision problem of how many pairs of skis to order. What is the best decision from an expected value basis?
in a general population what is the probability of your classmate being male?using the data collected from the student
the purpose of an automobile timing belt is to provide a connection between the camshaft and the crankshaft. this
This linear regression model was fitted to a sample of size 50 to produce the following regression equation: yhat = 145 + 1.2x1 + 300x2.
Scientist decided to do a study on the population growth of rabbits. Inside a controlled environment, 1000 rabbits were placed - how many rabbits would be there
Point is uniformly distributed in the unit sphere in three dimensions. a) Determine the marginal densities of the x, y, and z coordinates.
Who are also athletes but who are not regularly hit in the heads. Is this an example of an experimental or a non-experimental study? Why?
The standard errors for the OLS coefficient estimates are in parentheses. (Note: You might have already noticed that many research papers choose to report the standard errors for the coefficients instead of the t-statistics.)
Construct a hypothetical 95% confidence interval for a hypothetical case
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