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Question 1: Let X = (-5, 10]. Give atleast 3 σ-algebras on X. Provide proof or solution showing that each set contains the properties of a a-algebra on X.
Question 2: Define at least 5 sets A ⊂ R such that |A| = 5. Provide proof or solution showing that each set has outer measure 5.
Question 3. Suppose f: [0, 4Π] → R is defined by f (x) = cos x. Identify f-1(A) for the following:
a. A = (0, ∞)b. A = [0,1]c. A = (1)d. A = (2,3)
Question 4: Determine at least 3 S-measurable functions. Explain why these functions are S-measurable.
To determine the number of deer in a game preserve, a person catches 479 deer, tags then and lets them loose. Later, 561 deer are caught; 187 of them are tagged. How many deer are in the preserve?
Consider a particular genetic disease affects
Another offers 6.75% compounded continuously. Which investment will earn more interest in 5 years? How much will the better plan earn?
A football player runs for 1044 yards in 2000 and for 970 yards in 2004. Find the average rate of change in his performance.
Use implicit differentiation to find an equation of the tangent line to the hyperbola at the point (6, 8)?
a boxs inside measurements are 30 cms 24 cms and 15 cms. how many cubes can fit in the box with an edge of 3 cms?a box
Which of the following is not a source of technological advancement for a producer? better trained workers, more efficient physical capital, higher skill level of managers or outsourcing some aspect of production
How many pairs of each style should be produced per day to obtain maximum profit? Find the maximum daily profit.
Show that there are at least nine freshmen, at least nine sophomores, or at least nine juniors in the class.
Let v1 and v2 be vectors in R^n. Show that (prove) the set of all vectors w, an element of R^n such that w is orthogonal to both v1 and v2, is a subspace of R^n.
Two cylindrical tanks A and B such that it takes less work to pump the water from tank A to a height of 10 meters than from tank B.
's salary is 1 cent/second for a 40 hour work week. Tiare's salary is $1400 for a 40 hour work week. Who has a higher salary?
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