--%>
Assignment Help - homework help

Analysing the Probabilities

1. In the waning seconds of Superbowl XLVII, the Baltimore Ravens elected to take a safety rather than punt the ball. A sports statistician wishes to analyze the effect this decision had on the probability of winning the game.

(a) Which two of the following probabilities would most help the statistician perform his analysis? P(Win¦Safety); P(Safety¦Win); P(Punt¦Win); P(Win¦Punt); P(Win); P(Win∩Safety), P(Win∩Punt)?

(b) Define (in words) what the probabilities that you selected in part (a) mean and explain (in words) why they would be useful to the analysis.

2. Let A1;A2, and A3 be events in Ω. Show that P(A1 ∩ A2 ∩ A3) = P(A1¦A2 ∩ A3)P(A2¦A3)P(A3).

3. Let A and B be events such that P(A) > 0 and P(B) > 0. Show that P(AjB) = 1 - P(A¦B)

4. A business is keeping track of how many of two parts A and B are ordered, and whether those orders are completed on time or late. The data is in the table below.

1373_mandeep.png

(a) Find c1 and c2.

(b) Do type of part ordered and delivery time appear to be independent?

(c) A customer calls and angrily complains that the part he ordered was late without giving any more details. Which type of part did the customer most likely order?

5. A medical company is developing a new test for breast cancer. Based on lab results, the test appears to have 90% specicity (the percentage of all women without the disease that the test correctly identies) and 95% sensitivity (the percentage of all women with the disease that the test correctly identies). Suppose that 12% of women who take this test have breast cancer.

(a) What is the false positive rate for this test?

(b) What is the false negative rate for this test?

(c) How will the false positive and false negative rates for this test be a ected if the percentage of women with breast cancer decreases?

6. An urn contains a red ball, a white ball, a green ball, and a plaid ball. A single ball is randomly drawn from the urn. Let A be the event that either the red ball or the plaid ball is drawn, let B be the event that either the white ball or the plaid ball is drawn, and let C be the event that the green ball or the plaid ball is drawn.

(a) What is P(A υ B υ C)?

(b) Are A, B, and C independent from each other?

(c) Are A, B, and C mutually independent?

7. You have two decks of cards in front of you. One deck is a standard 52 card deck with four aces. The other also has 52 cards, but eight aces instead of four. You randomly choose a deck and draw two cards without replacement.

(a) What is the probability of drawing at least one ace?

(b) Given that you drew at least one ace, what is the probability that you drew from the standard deck?

 

 

 

   Related Questions in Advanced Statistics

  • Q : Probability Distributions and Data

    1. A popular resort hotel has 300 rooms and is usually fully booked. About 4% of the time a reservation is canceled before 6:00 p.m. deadline with no penalty. What is the probability that at least 280 rooms will be occupied? Use binomial distribution to find the exact value and the normal approxi

    		•
  • Q : Probability of Rolling die problem A

    A fair die is rolled (independently) 12 times. (a) Let X denote the total number of 1’s in 12 rolls. Find the expected value and variance of X. (b) Determine the probability of obtaining e

    		•
  • Q : Problem on utility funtion probability

    Suppose that your utility, U, is a function only of wealth, Y, and that U(Y) is as drawn below. In this graph, note that U(Y) increases linearly between points a and b.  Suppose further that you do not know whether or not you

    		•
  • Q : Problem on income probability Kramer

    Kramer spends all of his income  $270  on two products, soup (S) and on golf balls (G). He always bought 2 golf balls for every 1 cup of soup he consumes. He acquires no additional utility from the other cup of soup unless he as well gets 2 more golf balls a

    		•
  • Q : MANOVA and Reflection Activity 10:

    Activity 10: MANOVA and Reflection 4Comparison of Multiple Outcome Variables This activity introduces you to a very common technique - MANOVA. MANOVA is simply an extension of an ANOVA and allows for the comparison of multiple outcome variables (again, a very common situation in research a

    		•
  • Q : Analyse the statistics of the data

    Assigment Question Select any two manufacturing companies and formulate the cost and revenue functions of the companies. analyse the statistics of the data and then sketch the functions and determine their breakeven points. (Note: You are required to interview the production and sales manag

    		•
  • Q : Random variables Random variables with

    Random variables with zero correlation are not necessarily independent. Give a simple example.    

    		•
  • Q : Probability and Statistics

    Instructions: Do your work on this question and answer sheet. Please print or write legibly, and, as always, be complete but succinct. Record your answer and your supporting work in the designated space. Explain your method of solution and be sure to label clearly any

    		•
  • Q : Calculate confidence interval A nurse

    A nurse anesthetist was experimenting with the use of nitronox as an anesthetic in the treatment of children's fractures of the arm.  She treated 50 children and found that the mean treatment time (in minutes) was 26.26 minutes with a sample standard deviation of

    		•
  • Q : Statistics A nurse practitioner working

    A nurse practitioner working in a dermatology clinic is studying the efficacy of tretinoin in treating women’s post partum abdominal stretch marks. From a sample of 15 women, the mean reduction of stretch mark score is -0.33 with a sample standard deviation of 2.46. Describe what happens to the c

    		•