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Give examples to show that the finiteness of the collections in parts c and d is essential.
a) For any finite collection G1, G2, ...., Gn of open sets, intersection (at the top of the intersection sign is n and at the bottom is i=1) of Gi is open.
b) For any finite collection F1, F2, ...., Fn of closed sets, union sign (with n at the top of the sign and i=1 at the bottom) of Fi is closed.
Discuss an example of a way you use, or can use, a system of equations in your life? Describe a situation where a system of equations has no solution, and prove it mathematically.
Probability of Having a Disease when Testing Positive. Suppose that 1% of all people have a particular disease. A test for the disease is 99% accurate. This means that a person who tests positive for the disease has a 99% chance of actually having..
Find the probability of 14 or more widowed people in a random sample of 290 bowling league members?
Let C denote the circle |z| = 1, taken counterclockwise, and use the following steps to show that By using maclaurin series for e^z write the above integral as
Indicate, by checking the appropriate box, whether the given points below are on line 1 , on line 2 , on both line 1 and line 2 , or on neither one of the two lines:
Probabilities of Selecting Multiples of Fixed Numbers. Let N = 1000 and let S = {1, 2, ... , N}. Let D_i = {m belongs to S: i|m} for integers i between 1 and N.
A coin is flipped eight times where each flip comes up with either heads or tails how many possible outcomes?a) contain exactly 3 heads
Find the critical value at the 0.05 level of significance for a goodness of fit test if there are 6 categories?
Objective question based on probability distribution.
The following is offered as a solution of the equation. Because 7 = -12 is not a true equation, the equation has no solution. If this is correct, state that there is no solution. If not, explain in detail why it is not correct, and supply the corre..
Decision analysis with sample information/expected value/utility analysis/quantitative methodsProblem:A television network has been receiving low ratings for its programs.
Given f(x)=x^3 on [0,1] and the partition P={0,1/8,1/3,2/3,1}, find four different Riemann sums R(f,P). Show that Chi_Q is discontinuous at every point where Chi_Q is the characteristic function for Q - Rational numbers.
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