## Answers to ExercisesforSection 2: Probability Density Functions: Uniform, Exponential, Normal, and Beta

 1. Continuous Random Variables and Histograms 2. Probability Density Functions: Uniform, Exponential, Normal, and Beta 3. Mean, Median, Variance and Standard Deviation Calculus and Probability Main Page "Real World" Page

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

 1. Continuous Random Variables and Histograms 2. Probability Density Functions: Uniform, Exponential, Normal, and Beta 3. Mean, Median, Variance and Standard Deviation Calculus and Probability Main Page "Real World" Page