To prove: The statement “ | a b | = | a | | b | ”

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Chapter A, Problem 65E

To determine

To prove: The statement “ |ab|=|a||b|”

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2. Let (, F, P) be a probability space. Let X, Y be two independent ran- dom variables such that 1 3 P(X = 0) P(X = 1) P(X = 2) P(X = 3) P(X = 4) 10 10 5' 3 P(Y = 0) P(Y = 1) 10 1 10 7 1 P(Y2) = P(Y = 3) , P(Y = 4) 10 20 20 (i) Find the probability generation function Gx(s) and Gy(s) of X and Y, respectively. [12 Marks] (ii) Using Gx(s) and Gy(s), find the mean and variance of X and Y. [12 Marks] (iii) Find the probability generating function Gx+y(s) of X + Y. [8 Marks]

3. (i) Using the definition of the line integral of a vector field, calculate the line integral L³ F.dy of the vector field F: R² → R² given by F(x, y) = (y, x), and where the curve & is the unit semi-circle centred at the origin, located in the upper half-plane and oriented in the anticlockwise direction. Hint. Represent the curve y as the join of two curves y = 71 + 1/2 (see Example 8.9 in the Notes). [20 Marks] (ii) Calculate the same integral using Green's Theorem. [10 Marks]

1. Evaluate the integral ↓ f(x, y)dxdy, of function f R² →R over the domain DC R2, where: f(x, y) = 2x + y and D is the is the triangle with vertices (0, -1), (1,0) and (0,2). Hint. Represent D in the form D = {(x, y) = R² : x = (a, b), g(x) < y < h(x)} for some a

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Chapter A, Problem 65E

To determine

To prove: The statement “ |ab|=|a||b|”

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Answer 3

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Chapter A, Problem 65E

To determine

To prove: The statement “ |ab|=|a||b|”

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Answer 4

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Chapter A, Problem 65E

To determine

To prove: The statement “ |ab|=|a||b|”

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Answer 5

Chapter A, Problem 65E

To determine

To prove: The statement “ |ab|=|a||b|”

Answer 6

Chapter A, Problem 65E

To determine

To prove: The statement “ |ab|=|a||b|”

Answer 7

Chapter A, Problem 65E

To determine

To prove: The statement “ |ab|=|a||b|”

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Ch. A - Prob. 1E Ch. A - Prob. 2E Ch. A - Prob. 3E Ch. A - Prob. 4E Ch. A - Rewrite the expression without using the...Ch. A - Prob. 6E Ch. A - Prob. 7E Ch. A - Prob. 8E Ch. A - Rewrite the expression without using the...Ch. A - Prob. 10E

To prove: The statement “ | a b | = | a | | b | ”

Solution Summary: The author explains that the statement is proved by rewriting the equation as, c

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To prove: The statement “ |ab|=|a||b|”

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