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Given a 3 × 3 matrix Sigma:
a. Show that Sigma=cov(matrix(rnorm(30),nrow=10)) defines a proper covariance matrix.
b. Show that setting A=t(chol(Sigma)) leads to a simulation from Np(0, Σ) by using the command x=A%*%rnorm(3).
c. Compare the execution times of this approach and rmnorm when simulating one vector and 100 vectors.
Select a random variable to represent the category. Produce a probability mass function for that variable, and use it to compute the mean, the median and the variance of the data in the data set. Show the probability mass function, both in tabular..
suppose three players play a fair series of games under the condition that the first player to win three games wins the
Two new york designs are under consideration for possible adoption in an assembly plant. A time study is conducted with 10 workers using design 1, and 12 workers using design 2. The means and standard deviation of their assembly times in minutes a..
There are many examples of data mining methods being applied to business problems. But data mining methods are not only applicable to business problems. You are to research and cite at least three non-business areas where data mining might be frui..
The price of XYZ Corporation stock is normally distributed all through the year with mean of $42.00 per share and a standard deviation of $2.25 per share. Suppose that the stock is traded 240 days out of the year.
Provide SPSS output for the selected test and (where specified) write up the results in APA format as you would for a journal article.
State the relevant null and alternative hypotheses and calculate the appropriate test statistic. (By hand or using JMP.)
If a recent news report indicated that out of 105 people polled, 65 men and 15 women had given the president a high approval rating, while 15 men and 10 women had given the president a low approval rating. A chi-square test yields these resul..
What is the probability of a fatal accident over a lifetime? Explain your reasoning carefully. Hint: Assume independent events. Why might the assumption of independence be violated?
Use Chebyshev's theorem to find what percent of the values will fall between 120 and 150 for a data set with mean of 135 and standard deviation of 7.5
Test the claim that the actual amount of coke exceeds 12 ounces. (Note: You can use the value of $s$ as the value of $sigma$ for your hypothesis test).
At the 0.05 level of significance, is there sufficient reason to believe that the integers are not being generated uniformly?
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