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Let A = J+ X J+, where J+ is the set of positive integers.
Define a relation in A as follows: If (m1, n1) and (m2, n2) are elements in A, then (m1, n1) if m1,n2 = n1,m2. Show that is an equivalence relation and describe its equivalence classes.
Comment briefly on the difference in answers between part d and part e. What important assumption regarding independence makes these answers different? Which assumption do you think is more realistic? Why?
Suppose that B1, B2,......... ω ∈ Ω is a sequence of independent events such that for all i, P[Bi] = 1/2. Show that for any n ≥ 1 and for any ω ∈ Ω, we haveP[{ω}] ≤ 1/2n
3.84 Bias and variability. Figure 3.15 (on page 222) shows histograms of four sampling distributions of statistics intended to estimate the same parameter. Label each distribution relative to the others as high or low bias and as high or low vari..
Simulate the birthday problem to find the first person with the same birthday as yours. Perform the simulation 500 times. How many people did it take to find the first match? Was it typically about the same as the theoretical expected value?
Calculate the mean, median of the following grade point averages
i. suppose an influenza epidemic strikes a city. in 10 of families the mother has influenza in 10 of families the
A recent study of minimum wage earners found that 51.3% of them are 16 to 24. suppose a sample of 600 minimum wage earners is selected. is it appropriate to use the normal approximation to the binomial distribution.
Construct a 95% confidence interval for the population mean, μ. assume the population has a normal distribution. In a random sample of 26 computers.
A brand name has a 60% recognition rate. If the owner of the brand wants to verify that rate by beginning with a small sample of 10 randomly selected consumers, find the probability that exactly 6 of the 10 consumers recognize the brand name.
Six employees who have formed a car pool. If only four of these employees can drive, how many possible seating arrangements are there for the group?
Make a worksheet in Excel for your calculations. (b) Make a histogram of the data. Would you be justified in using a parametric t test that assumes normality? Explain.
The important thing is having a reason for picking the model that you decide on. You should choose a model for overall characteristics like a high R^2 value. Y
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