CALCULUS: EARLY TRANS. (LL)W/WEBASSIGN
CALCULUS: EARLY TRANS. (LL)W/WEBASSIGN
8th Edition
ISBN: 9780357019788
Author: Stewart
Publisher: CENGAGE L
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Chapter A, Problem 60E
To determine

To solve: The equation for x.

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3. (i) Let A, B, C, D, E be positive constants. Find the limit n³ D lim A(BC)³ +1 en 4+E. n→∞ [6 Marks] (ii) Let X be a random variable with the standard normal distribution, i.e. X has the probability density function Let 1 f(x) √2π n3x2 Xn = 100(50 +X6) en³4, n = 1, 2,..., 3+1 (a) Find the limit lim∞ Xn, verify your answer. Y = 100(50 +X) 22. [6 Marks] (b) Is Xn≤Y? Verify your answer. [6 Marks] (c) Is EY∞o? Verify your answer. [6 Marks] (d) Does lim∞ EXn (e) Find lim∞ EXn. Elim Xn? Why? [6 Marks] [3 Marks]
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]

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CALCULUS: EARLY TRANS. (LL)W/WEBASSIGN

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