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Let f be a Lipschitzian function on X and E a subset of X where f L on X is the same as for its restriction to E . Let x ∈ X \E . Does f on E uniquely determine f on X?
(a) Prove that the answer is always yes if x is in the closure E of E.
(b) Give an example where the answer is yes for some f even though x is not in E.
(c) Give an example of X, E, f , and x where the answer is no.
Assume that the joint probability density function of X and Y is given by? Find the marginal probability density function of X.
1. Let the population be given by {1, 2, 3}. Let p(x) = 1/3 for x = 1, 2, 3. Take samples of size 3 with replacement. (a) Calculate μ and σ2. (b) Obtain the sampling distribution of the sample mean.
Once production is set up, 80 units can be produced per day. Daily demand rate for the units is 60 per day. a. What is the most economical number to produce per production run? b. How long is each production cycle?
1. a researcher examines the records of all registered voters in one city and finds that 43 are registered democrats.
heights of men on a basketball team have a bell shaped distribution with a mean of 173cm and a standard deviation of
A standard deviation of 36 donuts. If a sample of 16 stores results in a sample average of 249 donuts what is the standard error of the mean?
Show that if S has more than one point, a separated uniformity never converges as a filter for its product topology.
The mean of a normal distribution is 400 pounds. The standard deviation is 10 pounds. a) what is the area between 415 pounds and the mean of 400 pounds?
For the following ANOVA experiments, determine the critical region(s) and critical value(s) that are used in the classical approach for testing the null hypothesis
One definition of a low-mileage car is one that is 4 years old and has been driven less than 45,000 miles. What percent of the cars returned are considered low-mileage?
Test the hypothesis that the baby's birthweight is independent of the mother's age.
consider rolling two fair dice one green and one red. let r be the random variable which determines the face value of
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