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For each statement, state whether it is true or false. Be sure to justify your answer.
a) Suppose you are given a linear program in Rn with mE equality constraints and mI inequality constraints. Let x be an element of the polyhedron at which n - mE inequality constraints are active. Then x must be an extreme point of the polyhedron.
b) If an LP has more than one optimal solution, and has an optimal extreme point, then it must have at least two optimal extreme points.
c) Let S be a subspace in Rn and {x1, x2, ..., xn} be a set of vectors whose span is S. The only vector d such that the cross product of d and xi is 0 for all i = 1, 2, ..., n is the zero vector.
State the main points of the Central Limit Theorem for a mean. Why is population shape of concern when estimating a mean? What does sample size have to do with it?
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Assume the probability that a telephone in any given telephone booth is defective is 0.2. Determine the probability that if 8 phone booths are examined, the number of defective phones is exactly 3.
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If the p value for a test for difference of educational level of two groups is p=0.0184, is the difference statistically significant at the 0.01 level?
a population is normal with a variance of 17. suppose you wish to estimate the population mean u. find the sample size
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