Let (Ω,F,P) be a probability space. Recall the R.V. X is called simple, if there exist A₁, …., Aₙ ∈ F and b₁, …, bₙ ∈ R such that X = ᵢ₌ₗ∑ⁿ bᵢ 1{A ᵢ }. Note that A; need not be disjoint. ...) ... a) Show that if R.V. X,Y are simple, then so is the linear combination aX + bY. b) Is it true that if X₁, X₂ are all simple then so are X₁ + X₂, and X₁ ∧ X₂ = min X1, X₂? c) Is the representation of X (i.e. the sets A₁,.., Aₙ and the scalars b₁, ..., bₙ) unique? d) What if Aᵢ are known to be disjoint? How many values can X take then? e) Show that R.V. X is simple if and only it takes finitely many values. f) Show that E[X] is well defined for X simple R.V.. In other words, if X has two representations: X = ᵢ₌ₗ∑ⁿ bᵢ 1{Aᵢ } and X = ᵢ₌ₗ∑ᵐ Cᵢ 1{Bᵢ), such that B₁, ..., Bₘ ∈ F and C₁, ..., Cₘ ∈ R, then we must have ᵢ₌ₗ∑ⁿ Bᵢ P(Aᵢ) = ᵢ₌ₗ∑ᵐ cᵢP(Bᵢ).

What is the ratio of 33/36

CAN SOMEONE ANSWER THIS PLEASEMargie bought 1 1/2
pounds of tomatoes for $2.00 per pound,
1/4 pound of onions for $1.60 per pound, and 1 pound of apples for $1.65 per pound. How much did she pay for her total purchase?

If a chicken farm sold 3,000 dozen eggs last week, how many individual eggs were sold?A. 36,000
B. 250
C. 3,000
D. 3,600

That you're positive that you should be trying out these difficult math questions, let’s get right to it! The answers to these questions are in a separate section below, so you can go through them all at once without getting spoiled.#1:

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body_ACT_0809_-_55-1



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body_ACT_0809_-_56



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body_ACT_0809_-_57-1



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body_ACT_0809_-_60



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body_ACT_1112_-_51-1



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body_ACT_1112_-_52



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body_ACT_1112_-_58



#15:

body_ACT_1314_-_55-1

What is the solution of the equation? 17=2/3n+3

A football is kicked toward the goal. The height of the ball is modeled by the function h(t) = -16t2 + 64t where t equals the time in seconds and h(x) represents the height of the ball at time t seconds. What is the axis of symmetry and what does it represent? t = 2; it takes 2 seconds to reach the maximum height and 2 seconds to fall back to the ground
t = 2; it takes 2 seconds to reach the maximum height and 4 seconds to fall back to the ground
t = 4; it takes 4 seconds to reach the maximum height and 4 seconds to fall back to the ground
t = 4; it takes 4 seconds to reach the maximum height and 8 seconds to fall back to the ground