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Let K be the Tychonoff-C? ech compactification of R. Show that addition from R × R onto R cannot be extended to a continuous function S from K × K into K . Hint: Let xα be a net in R converging in K to a point x ∈ K \R. Then -xα converges to some point y ∈ K \R. If S exists, then S(x, y) = 0 ∈ R. Then by Problem 4 there must be neighborhoods U of x and V of y in K such that S(u, v) ∈ R and |S(u, v)| <>1 for all u ∈ U and v ∈ V . Show, however, that each of U and V contains real numbers of arbitrarily large absolute value, to get a contradiction.
the breaking strength of threads has a standard deviation of 18 grams. how many measures on breaking strength should be
A box contains ten fuses of which 3 are defective. Two fuses are selected at random from the box without replacement. What is the probability that exactly one of the fuses selected is defective?
Find the confidence interval for the mean price, μ, of all dealer sticker prices of new cars: for a confidence level of 90% in thousands of dollars:
Shoppers enter Hamilton Place Mall at an average of 120 per hour, and the number and shoppers is Poisson distributed. What is the probability that at least 5 shoppers will enter the mall between 5:00 and 5:05 p.m.?
1.a sample of 50 male and 50 female infants were put on an experimental infant formula. after two weeks the parents of
Compare the mean of the sampling distribution of sample means with that of the population.
q1. statistics plays a vital role in almost every facet of human life. describe the functions of statistics. explain
Define the parameter of interest, state the null and alternative hypotheses corresponding to the researchers' questions. Compute the test statistics corresponding to the hypothesis
the correlation between the temperature in celsius and temperature in fahrenheit.the correlation between hours of sleep
heights of men on a baseball team have a bell shaped distribution with a mean of 184 cm and a standard deviation of 5
there are 1000 students in the senior class at a certain high school. the high school offers two advanced placement
chi-squared a study is designed to investigate whether there is a difference in response to various treatments in
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