Let T be a linear transformation that maps Rn onto Rn. Show that T-1 exists and maps Rn onto Rn. Is T-1 also one-to-one? If so, prove it. If not, prove that instead.
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Paleomagnetic studies of Canadian volcanic rock known as the Carmacks Group have recently been completed. The studies revealed that the northward displacement of the rock units has an approximately normal distribution with standard deviation of 50
In the Fall semester of 2011, 48.1 % of students at UTA were women. Suppose that two students from UTA are selected at random. Using the probability tree method, calculate: The probability of getting exactly one woman.
Almost all medical schools in the United States require applicants to take the Medical College Admission Test (MCAT). On one exam, the scores of all applicants on the biological sciences part of the MCAT were approximately Normal with mean 9.9 and
The number of spam emails received each day follows a Poisson distribution with a mean of 50. Approximate the following probabilities. Round your answer to four decimal places (e.g. 98.7654).
If they stop play when the first players needs one game while the second and third players each need two games, find the fair division of the stkeas. (This probem was discussed in the cprrespondence between Pascal and Fermat)
A quality engineer is monitoring a lens coating process, where a lens is either a high quality lens or not a high quality lens, and the monitoring process meets the conditions for a binomial experiment. The probability a lens is a high quality len
In a region, 80% of the population have brown eyes. if 13 people are randomly selected, find the probability that at least 11 of them have brown eyes.
In the second community, a random survey of 90 households showed the mean household size was 4 with a standard deviation of 6. Assuming a significance level of .01, test the hypothesis that the two communities are statistically equivalent with res
One of Mendel's breeding trials came out as follows. Make a Chi-square test to see whether these data were fudged.
A client gives you a data set of 30 observed values that represent the number of gallons of gas that 30 individual Nissan Sentra owners purchased at the gas pump last month. Your client wants to know if the data set represents a normal distributi
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