Let a random sample be taken of size n = 100 from a population with a known standard deviation of σ
= 20. Suppose that the mean of the sample is = 37. Find the 95% confidence interval for the mean, μ
, of the population from which the sample was drawn. (Answer in CI format and round the values to whole numbers.)
5
19
20
1
What will be the first item the burglar should choose? (Please show your work by stating your reason.)
a. Item 1
b. Item 2
c. Item 3
d. Item 4
e. Item 5
2. Let Dn be the dihedral group of symmetries of a regular n-gon, and let Cn ⊂ Dn be the subgroup of rotations. Let also H ⊂ Cn be an arbitrary subgroup. Prove that H is a normal subgroup of Dn.
Remark: H is a subgroup of Cn, so it is also a subgroup of Dn. Note that H is a normal subgroup of Cn, because Cn is Abelian. This means that ghg−1 ∈ H for any g ∈ Cn. What you need to prove is a stronger result: H is normal in Dn, meaning that ghg−1 ∈ H for any g ∈ Dn, and not only for any g ∈ Cn.
Hint: One possible approach is to show that for any element g ∈ Dn, the set gHg^-1 = {ghg^-1 | h ∈ H} is a subgroup of Cn. What is the order of this subgroup?
What do we know about subgroups of cyclic groups? Another approach is to use geometric arguments to prove that for any reflection g ∈ Dn Cn and any rotation r ∈ Cn, one has grg^-1= r^-1.
2. Let consumption equal C = 100 + 0.75Y. The equilibrium condition is that income (Y) equals planned expenditures, or Y = C + I, where I is investment.
a. Solve for equilibrium levels of income and consumption if I = 500.
b. Find reduced-form equations for Y* and C* in terms of the exogenous variable, I.
c. Describe the comparative statics results of this system with respect to changes in I.
Let C_b(R) denote the space of all bounded, continuous functions f : R → C. Let C_0(R) denote the set of continuous functions f : R → C for which lim x→±∞ f(x) = 0. How do you prove that C_b(R) and C_0(R) are complete in the uniform metric?
Let C(x) be the cost to produce x widgets, and let R(x) be the revenue.
(a) graph both functions
(b) find the minimum break-even quantity
(c) find the maximum revenue
(d) find the maximum profit
R(x) = -x2 + 8x, C(x) = 4x + 3
the question statement is in the picture………………………..
Let C he the curve [cee[1’rt2} + tweet“—tll — ein[1’ttf2]} fur Be at and let 2 [391+ms[x+y})i—cas{x+y}j. Find] F- 11115. (Hint: recall thatn= (d5,— —%}.}c Evaluate the line httegrali lxy :11: + 1:2 11y where C’ 15 the curve 1:111 the cardiad1*: 2 + cos B traveled counterclockwise
Let C be the curve of intersection of the parabolic cylinder x^2 = 2y, and the surface 3z = xy. Find the exact length of C from the origin to the point (4, 8, 32/3).
Let C be the curve of intersection of the parabolic cylinder x^2 = 2y, and thesurface 3z = xy. Find the exact length of C from the origin to the point (4, 8, 32/3).Let C be the curve of…
Let C" be a set in three – dimensional space and let @ IC" ) be equal to the volume of C. if Chas finitevolume ; otherwise . let @ !C’ ; be undefined . Find @Icj .( a) ( = (1 2. 4. 2 ) ERY : D < < < 2, 0 = 4 5 1, 0 < < < 3)`( b ) C = ( ( 2. 4. 2 ) ERS : 12 + 4 2 + 2 2 2 1).
Please help with Probability Space functions. The problem is shown in the attachment. I was struggling in understand the concept and I’ll be grateful if you can show me the steps to solutions. Thanks in advance!
6. Let C" be a set in three – dimensional space and let @ ( C ) be equal to the volume of C , if Chas finite*volume ; otherwise , let Q ( O’; be undefined . Find Q ( 0) .( a ) (" = ( ( 2 , 4 , 2) ERS : 0 < < < 2, 0 < 3 < 1 , 0 < < < 3 ).( b ) C = ( ( 2 , 3 , 2) ER 3 : 2 2 + 3 2 + 2 2 2 1 ).7 . For every one – dimensional set C for which the integral exists , Q ( C ) = [of (a ) do , where f ( a ) -Gx ( 1 – 2 ) , 0 < < < 1 , zero elsewhere ; otherwise , let @ ( C") be undefined . Find Q ( C" ) .( a ) (1 = PIER : 1 / 4 < < < 3 / 4)( b ) C 2 = ( 1 / 2}( C ) C3 = PIER : 0 < < < 1018. Suppose the experiment is to choose a real number at randomandom in the interval ( 0 , 1 ) . For any subinterval( a, 6) C ( 0 , 1 ) , it seems reasonable to assign the probability P [ ( a , 6) ] = 6 – a; i.e., the probability ofselecting the point from the subinterval is directly proportional to the length of the subinterval . If thisis the case , choose an appropriate sequence of subintervals to shoe that P [ [a] ] – O for all at ( 0 , 1 )Hint : let ( Chin =I may be a decreasing sequence of events , as in Question 2 , then limn_* too P ( On ) -P ( limn_ too On ) = P (17 = 1 On )`
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