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Peano curves
Show that there is a continuous function f from the unit interval [0, 1] onto the unit square [0, 1] × [0, 1]. Hints: Let f be the limit of a sequence of functions fn which will be piecewise linear. Let f1(t ) ≡ (0, t ). Let f2(t ) = (2t, 0) for 0 ≤ t ≤ 1/4, f2(t ) = (1/2, 2t - 1/2) for 1/4 ≤ t ≤ 3/4, and f2(t ) = (2 - 2t, 1) for 3/4 ≤ t ≤ 1. At the nth stage, the unit square is divided into 2n · 2n = 4n equal squares, where the graph of fn runs along at least one edge of each of the small squares. Then at the next stage, on the interval where fn ran along one such edge, fn+1 will first go halfway along a perpendicular edge, then along a bisector parallel to the original edge, then back to the final vertex, just as f2 related to f1. Show that this scheme can be carried through, with fn converging uniformly to f .
For the passengers in the SRS, what is the approximate probability that the mean length of time for them to get through security will be less than 18 minutes?
If the card selection is without replacement, what is the probability that the first card is an ace and the second card is also an ace? (Express the answer in simplest fraction form)
the probability to catch disease a is 10. the probability to get disease b is 17. the probability to get at least one
Estimate the regression parameters, the infant mortality rate for a country with a net food supply of 2900 calories per person per day, and draw the regression line on the same graph with the scatter diagram.
Clearly a straight line model does not accurately describe what is going on with this data. Does this mean there is no relationship between income and time?
A regression equation was computed to be Y'=35+ 6X. The value of the 35 indicates that
If we wanted to shorten the interval of the estimation of the true mean of Saturday sales to a width of $600 in total, what should the size of our sample be to achieve it?
A random sample of 40 part time workers has a mean annual earnings of $3120 and a population standard deviation of $677. Compute the 95% confidence interval for the mean.
a town has 20 000 registered voters of whom 8800 are democrats. a survey organization takes a simple random sample of
Group 2 data [ 141, 139, 172, 131, 150, 125. Assume normal distribution, with equal variance in the two groups and conclusion for a=0.05.
the following 10 observations of variables x and y were collected.x 1 2 3 4 5 6 7 8 9 10y 25 22 21 19 14 15 12 10 6
mimi just started her tennis class three weeks ago. on average she is able to return 15 of her opponents serves. if
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