tabular19

Point values are as indicated. As usual, you must show your work to receive full credit.

  1. 25 pts.
    You have three friends on the board of directors of a certain company. There are twelve board members altogether. Four of the members are chosen randomly for a task force.

    1. What is the probability that none of your friends are chosen?
    2. What is the probability that all 3 of your friends are chosen?

  2. 20 pts.
    A sales person makes 300 calls during a three-month period. The probability of a sale on any given call is 1/4. Find the expected number of sales as well as the standard deviation, assuming Bernoulli trials model for this situation.

  3. 25 pts.
    A four number combination is needed to open a safe. Because of am eccentric manager's idea of security, the numbers are never written down; however the sum of the first three is 33, the sum of all but the third is 31, the sum of all but the second is 24, and the sum of the last three is 26. Using matrix row operations, find the combination to the safe.

  4. 25 pts.
    1. Let A and B be events in a sample space S. Assume A, B are undependent. P(A) = 3/4 and P(B) = 1/4. Find P(A B)
    2. P(A|B) = 1/2. Find P(A B)

  5. Bonus - 30 quiz points
    A random variable X has the possible values -1, 0, and 1, with probabilities p, q, and r respectively. The expected value of X2 is 4/5. Use the big-M method to find the largest possible value of the expected value of X. You may use M=10.(You will need two different artificial variables, but not slack or surplus.

  6. 30 pts.
    Assume y 2x ; x 3y; and x + y 12, where also x 0 and y 0. Using either the simplex method or a graph, find the maximum value of 2x + 3y

  7. 25 pts.
    An absorbing Markov chain had the following transition matrix:

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  8. 20 pts.
    1. Perform and indicate whatever row operations are needed to put

      tex2html_wrap_inline159

    2. If and ,
      Compute AB - BA.

  9. 25 pts.
    Suppose that a certain disease has the following properties. Each year the probability of any uninfected person becoming infected is 1/200, while each year any infected person is cured with probability 1/2. What is the long term probability that a given person will have the disease in a given year? (This is a Markov chain problem!)


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