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1a. If X and Y are infinite sets with the same number of elements, show that the following conditions are equivelent for a function f: X-->Y:
(i). f is injective(ii). f is bijective(iii) f is surjective
1b. Suppose there are 11 pigeons sitting in some pigeonhole. If there are only 10 pigeonholes prove that there is a hole containing more than one pigeon.
I just dont know where to begin with the proof and how to show this.
A standard IQ test has mean of 98 and a standard deviation of 16. We want to be 99% certain that we are 8 IQ points of the true mean. Determine the sample size.
Explain the concept of risk analysis and how monte carlo simulation can provide useful information for making decisions.
A survey is being planned to determine the mean amount of time corporation executives watch television. A pilot survey indicated that the mean time per week is 20 hours, with a standard deviation of 5.5 hours
What is the possible uses of regression and correlation analysis in doctoral-level research? Would I be able to use these techniques in my dissertation, or any application in other areas?
1. What do discrete random variables describe? 2. Explain joint probability. 3. Explain conditional probability.
A financial planner wants to compare the yield of income- and growth-oriented mutual funds. Fifty thousand dollars is invested in each of a sample of 35 income-oriented and 40 growth-oriented funds.
the maximum point total for the quarter was 200. The point totals for the 10 students are given in the stemplot below. For the density curve displayed below, which of the following is true?
A professor in the psychology department would like to determine whether there has been a significant change in grading practices over the years.
A researcher has reason to believe that, for an experiment with 50 points, a 95% prediction interval would be of width 4. If the researcher wishes to run a more precise experiment that will result in a 95% prediction interval of width 2, then the ..
Compute the 95% confidence interval around the mean of each of the three groups and plot the confidence interval in the space provided above.
An American put option to sell a swiss franc for dollars has a strike price of $0.80 and a time to maturity of one year. The volatility of the swiss franc is 10%
Test to see if the mean cell phone bill has changed since 2004. Use a .05 level of significance for the test.
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