Problem 3: Let Ω be a sample space, and P a probability on Ω. Suppose that B1, B2, B3 are pairwise disjoint, have positive probability, and their union is Ω. We let G := σ (B1, B2, B3) .
For a fixed set A ⊂ Ω, suppose that we have P(A|G) = 12IB2. Here, IB2 denotes the
indicator function of the set B2.
(a). Show that the random variable Y := P (A | G) is G-measurable.
Let F := 2Ω (the power set of Ω), and let H := {∅,Ω}.
(b). Is Y F-measurable? Why?
(c). Is Y H-measurable? Why?
(It is an intro to math finance course problem)

Restrictions on f(x) = 1/x+5 and g(x) = x-2

Brittany has designed four different birdcages, each with the same volume: a square pyramid, a cylinder, a cone, and a sphere. the zoo wants to use one of brittany’s designs but plans to change the volume of the cage. find the design change that would result in the birdcage with the greatest volume. increase the area of the base of the square pyramid by a factor of ten. increase the height of the cylinder by a factor of ten. increase the radius of the cone by a factor of ten. increase the radius of a sphere by a factor of ten. juan wants to build a greenhouse in his back yard. he needs to maximize the ratio of floor area to structure volume in order to provide the most room for plants while minimizing the area to be heated. find the description of the structure that best meets juan’s criteria. a cube with a side length of 12 feet a cone with a diameter of 12 feet and a height of 10 feet a square pyramid with a base side length of 12 feet and a height of 9 feet a hemisphere with a diameter of 12 feet marion has a bicycle that she is planning to take for a ride. the rim of the rear wheel lies 41 cm from the center of the wheel. the tire itself has a thickness of 3 cm.in order to marion to ride her bicycle 96,712 cm, approximately how many rotations will the rear wheel make? 350 15.9 376 5133 an isosceles trapezoid has perimeter of 42 inches. each of the congruent nonparallel sides is 5 inches long, and the trapezoid is 3 inches tall. how long are the two parallel sides? 10 inches and 16 inches 12 inches and 20 inches 16 inches and 16 inches 10 inches and 22 inches

Which of the following is true for the relation f(x)=2x^2+1