Probability and Statistics for Engineering and the Sciences (with CD-ROM and InfoTrac )

Info icon This preview shows pages 1–3. Sign up to view the full content.

Midterm Examination Solutions, Statistics 220, Fall 2005 19 October 2005 1 Binomial vs. Poisson X is a binomial random variable, n = 10, p = 0 . 1. Y is a Poisson random variable, λ = 1. (a) What is E [ X ]? (1 pt) What is Var ( X )? (1 pt) What is the probability that X = 2? (3 pts) (b) What is E [ Y ]? (1 pt) What is Var ( Y )? (1 pt) What is the probability that Y = 2? (5 pts) (a) The expectation of a binomial is np = 1. The variance is np (1 - p ) = 0 . 9. Pr ( X = 2) = 10 2 (0 . 1) 2 (0 . 9) 8 = 10 · 9 · 8! 2 · 8! (0 . 1) 2 (0 . 9) 8 = 45(0 . 1) 2 (0 . 9) 8 = 0 . 1937102 (b) The expectation of a Poisson is λ = 1. The variance is λ = 1. Pr (() Y = 2) = e - 1 1 2 2! = 0 . 1839397 2 Camels Bactrian camels ( Camelus bactrianus ) are used as beasts of burden in Central Asia. A survey of the camels available in a certain town in Afghanistan shows that their mean weight is 1600 pounds, with a standard deviation of 150 pounds. (a) What are the mean and standard deviation of the camels’ weights in kilograms? (2 pts) Hint : 1 kg = 2.2 lb. (b) The camels are now loaded with water casks weighing exactly 120 kilograms each. What is the mean and standard deviation of their total weight? (3 pts) (a) Multiplying the measurements by a constant multiplies the mean and the standard deviation by the same constant. So the mean weight is 727 kg, and the standard deviation of the weight is 68 kg. 1
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

(b) Adding a constant increases the mean by that amount, but doesn’t change the standard deviation. Mean loaded weight, 847 kg, standard deviation 68 kg. 3 Coins (a) What are the probabilities of getting the following sequences of heads and tails from 10 consecutive tosses of a fair coin? (2 pts) (i) HHHHHHHHHH (ii) HTHTHTHTHT (iii) HHTTTTTTHH (b) What is the probability of getting 0 heads in 10 consecutive tosses? 5 heads out of 10? 6 out of 10? (3 pts) (a) All three sequences are the same length, and every individual sequence of that length has the same probability. There are 2
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern