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# Introduction To Probability Models STAT 22500

Purdue

GPA 3.63

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This 7 page Class Notes was uploaded by Bailey Macejkovic on Saturday September 19, 2015. The Class Notes belongs to STAT 22500 at Purdue University taught by Staff in Fall. Since its upload, it has received 63 views. For similar materials see /class/207945/stat-22500-purdue-university in Statistics at Purdue University.

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Date Created: 09/19/15

STAT 225 Review Exam 2 Your name Your instructor s name Your class time circle one 730 830 930 1030 1130 1230 130 230 330 Note 0 Show your work on all questions Unsupported work will not receive full credit Decimal answers should be exact or to at least four significant digits You are responsible for upholding the Honor Code of Purdue University This includes protecting your work from other students You are allowed the following aids a onepage 8 12 x 11 handwritten in your handwriting cheat sheet a scienti c calculator and pencils Instructors will not interpret questions for you If you do have questions wait until you have looked over the whole exam so that you can ask all of your questions at one time You must show your student ID upon request and sign the class roster when you turn in your exam to your instructor Turn off your cell phone before the exam begins Points Possible Points Received 1 9 1 8 5 20 16 16 6 100 For a certain board game the moves are made by a spinner The spinner is equally likely to land in any of ten places The number on the place where you land indicates the number of spots you must move on the board Two of the places have a in which you must move one spot back on the board Four of the places have a 0 three have a l and one has a 2 Let X be the number of spots you must move after one spin a Fill in the numbers in the PMF below 4 pt b Find the probability that you do not move backward 3 pts c Find the expected value and variance of X 6 pts d Find Var2X 7 3 pts e 3pts Find P X2 g 1 l X 2 0 3 pts 2 Determine whether the following statements are true or false A statement is only true if it is always true 2pts each a EXZZEXZ T F b VarXYVarXVarY T F c If PX 0 PX l lthenX is a Bernoulli random variable T F d IfX is a Poisson random variable then it is possible thatPX l gt 0 T F e If X N Poissonl 01 and Y N Poissonl 03 then T F EXY 02 f If Y N HypergeometricNn p then N Z n T F g EX2VarXEX2 T F h IfXNGeometricpthen PX1gtPX2 T F 3 Suppose X and Y are random variables We know EX l EY l Var X 4 VarY 9 and CovXY 3 Find Cov 3X 2 4Y 5 pts 4 Suppose cats are brought into the humane society at a Poisson rate of three cats per day and dogs are brought in at a rate of one dog per day a What is the probability that fewer than three cats are brought in tomorrow 5 pts b What is the probability that exactly one dog and exactly three cats are brought in tomorrow 5 pts c What is the probability that they would have to wait exactly 7 days until the first day that exactly 4 animals ie dogs and cats combined are brought in 5 pts d What is the probability that fewer than three cats come in each day of the following week Assume one week is seven days 5 pts 5 X and Y are discrete random variables with the following joint PMF Use this information to answer the following questions X Y 1 0 1 2 2 001 005 011 004 1 008 002 006 012 0 013 009 003 007 1 002 003 010 004 a Find the marginal distribution for X 4 pts b Find PXY gt 0 4 pts 0 Find PXY gt 1 l X 1 4 pts d Are X and Y independent Justify your answer 4 pts 6 For each of the following random variables write down the name of the most appropriate distribution Note that the approximate distribution should be used whenever applicable Assume all turns of the key produce independent results You do NOT need to include the values of the parameters for full credit a You put the key in the ignition of your 1976 Chevy Nova X 1 if the engine starts X 0 if the engine does not start 2 pts b X is the number of times the engine will start out of the next 10 times Iturn the key 2 PtS c X is the number of times I have to turn the key until the engine starts for the 5Lh time 2 PtS d X is the number of accidents per year that involve a 1976 Chevy Nova 2 pts e X is the number oftimes Itry to drive my car until the car will not start 2 pts CD If there are 3 Chevy Novas and 5 Saturn Ions X is the number of Novas you test drive if you picked 3 sets of car keys randomly without replacement 2 pts If there are 3000 Chevy Novas and 5000 Saturn Ions X is the number of Novas you test drive if you picked 3 sets of car keys randomly without replacement 2 pts 00 V 7 V If there are 3000 Chevy Novas and 05 of all Chevy Novas have a defective transmission X is the number of those with a defective transmission 2 pts 7 A thirdgrade teacher rewards four students each with a bag of candy but allows them to eat only three pieces now Each bag of candy contains ve red candies seven yellow candies and ve white candies Each reaches into their bag and draws three pieces at random but none of them like the white candy Hence each student will continue to replace all three candies and redraw three new ones until there are no white pieces are in their sample One of the students Nolan has drawn at least one white in each of his rst eight sample draws Let W be the number of draws until he is successfully gets a draw with no white candies Using this information what is the probability that W is greater than 11 6 pts

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