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If (X, T ) is a locally compact Hausdorff space, show that X , as a subset of its Tychonoff-C? ech compactification K , is open (if f is the homeo- morphism of X into K given in the definition of Tychonoff-C? ech com- pactification, the range of f is open). Hint: Given any x ∈ X , let U be a neighborhood of x with compact closure. Show that there is a continuous real function f on X ,0 at x , and 1 on X \U . Use this function to show that x is not in the closure of K \U.
Assume that if a women carries the gene for haemophilia, any child has a 50% chance of inheriting that gene, and that is always clear whether or not a son has inherited the gene,
Assume the population standard deviations are not the same. At the .05 significance level, is there a difference in the mean waiting time?
the weight of a sophisticated running shoe is normally distributed with a mean of 12 ounces and a standard deviation of
At the .05 level, can we conclude-that women think men are less kind, gentle, and thoughtful in 2000 compared with 1990?
The standard deviation of the sample was 6.2 weeks. Construct a 95 percent confidence interval for the population mean. Is it reasonable that the population mean is 28 weeks?
as we have noted in previous chapters even a very small effect can be significant if the if the sample is large enough.
For large correlations, the SAS program simply states that p
the national high school sports database reports that players of lacrosse average 55 goals per season. the standard
consider an experiment in which our sample space is s1234567.also e1124 e223456 e37. describe the outcomes in each one
How variable is the number of service calls with which Sam's department must deal?
in a poll respondents were asked if they have traveled to europe. 68 respondents indicated that they have traveled to
q1.acid rain has caused many lakes to become more acidic. a lake is considered nonacidic if the ph level is greater
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