1 , mark 9. E and F are two events defined on sample space S, with Pr[E] = 0.5 and Pr[F] = 0.4. If it is known that Pr[EUF] = 0.8, which of the following statements is/are true? (i) E and F are independent events (ii) E and Fare mutually exclusive events A: Both. B: (i) only. C: (ii) only. D: Neither. E: Cannot be determined.

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15 Oct 2018

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1 5 mark . It is known that events E and F are mutually exclusive, with Pr[E] = 0.3 and Pr[F] = 0.5. Find Pr[Eºn Fº]. A: 0 B: 0.15 C: 0.85 D: 0.2 E: 0.8

PROBLEM 17: A sample space S has two independent events, A and B, with Pr[A] = 0.40, and Pr[BA] = 0.30. Which of the following represents Pr[A' B'l? A) 0.42 D) 0.12 B) 0.46 E) 0.28 C) cannot be determined because there is not N) none of the above (which means that the answer enough information given in the problem. can be determined, but it is not listed among the answer choices given).

48 f(x) = 12 + (x + 1)2 4. (22 pts) The function f, its derivative f', and its second derivative f" are given by the expressions below. f'(x) = -96(x+1) (12+(x + 1)2) (12+(x + 1)2) (a) Circle the correct statement. f"(x)288(x2 + 2x - 3) i. f is even ii. f is odd. iii. f is neither even nor odd. (b) Give an equation for each horizontal asymptote of f. Write "none" if appropriate. Show your work. Show work for parts (c), (d), (e), and (f) in the space below. (c) List the interval(s) on which f is increasing. Write "none" if appropriate. (d) List the interval(s) on which f is decreasing. Write "none" if appropriate (e) List the x-value(s) at which the local minima of f occur. Write "none" if appropriate (f) List the x-value(s) at which the local maxima of f occur. Write "none" if appropriate. (8) List the interval(s) on which f is concave up. Write "none" if appropriate. (h) List the interval(s) on which f is concave down. Write "none" if appropriate. (i) List the x-coordinate(s) of the inflection points of f. Write "none" if appropriate. () Sketch the graph of y = f(x). Mark the locations of any local extrema and/or inflection points with filled-in circles. Your sketch should be consistent with your answers to (a)-0). -10 -9 -8 -7 -6 -5 -4 4 5 6 7 8 9 10

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