for
Section 2: Probability Density Functions: Uniform, Exponential, Normal, and Beta
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1. Yes
3. No; the integral 1
5. No; the function is not 0
7. Yes
9. Yes
11. No; both conditions fail
13.1/4
15. ln 2
17. 1
19. exponential
21. normal
23. uniform
25. beta
27. exponential
29. 0.2
31. 0.5934
33. 0.6164
35 (a) 0.000 0010 (b) 1
37. 0.3829
39. 0.01654
41. 51.96%
43. Yes. The probability that a regional Bell had lower operating expenses than SBC was 0.2064. In other words, approximately 21% of the companies should have had lower operating costs than SBC (according to the normal distribution).
45. By the Fundamental Theorem of Calculus, F(x) as given is an antiderivative of f(x). In other words, F'(x) = f(x), as required.
47. By definition of F(x), F(a) = aa f(t) dt, which is zero because the lower and upper limits agree, and F(b) = ab f(t) dt = 1.
49. F(x) = (x10,000)/30,000
51. 1 e0.3x
53. 1 e0.000121x
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Stefan Waner (matszw@hofstra.edu) | Steven R. Costenoble (matsrc@hofstra.edu) |