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# Prob & Statistics Engineering STT 351

MSU

GPA 3.72

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This 10 page Class Notes was uploaded by Aryanna Jerde on Saturday September 19, 2015. The Class Notes belongs to STT 351 at Michigan State University taught by Nao Mimoto in Fall. Since its upload, it has received 144 views. For similar materials see /class/207814/stt-351-michigan-state-university in Statistics and Probability at Michigan State University.

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Date Created: 09/19/15

STT 351 HW on Chapter 2 Due Feb 1Wed Questions 1 Suppose that vehicles taking a particular freeway exit can turn right R7 turn left L7 or go straight The experiment is consisted of observing the direction for each of two successive vehicles a Write down he sample space S b List all outcomes in the event A that exactly one of two vehicles turn right c List all outcomes in the event B that two vehicles goes not go in the same direction d What is PA7 e What is PB g What is PA U B gt f What is PB h What is PA m B E0 00 r U 03 There are ve cards labeled ABCDE How many different sequence of letters can be constructed using 3 of those cards You are ipping a coin 5 times How many different ways are there for getting exactly 2 tails eg HHTHT If there are 8 balls in a box labeled 1 through 8 and 3 balls are taken out at once how many different outcomes are there If we repeat the same experiment as above but 5 of the balls in the box are red and 3 are white then how many different ways of getting two red and one white Consider randomly selecting a student at a certain university and let A denote the event that the selected individual has a Visa card and B be the event that the individual has a Master card Suppose a What is P At least one card b What is P Neither 7 C What is P Visa7 but not master 7 Certain system can experience three different types of defects Let Ai denote the event that the system has a defect of type 239 Suppose that PA1 12 PA2 07 PA3 05 PltA1UA2 PltA1UA3gt PltA2UA3 PltA1 Ag Ag a What is P System does not have type 1 defect b What is P System has both type 1 and 2 defects 0 What is P System has both type 1 and 27 but not type 3 defect d What is P System have at most two types defect 8 A certain sports car comes equipped with either an automatic or a manual transmis sion7 and the car is available in one of four colors Relevant probabilities for various combinations of transmission type and color are given in the table below Let A white blue black red Automatic 13 1 11 11 Manual 15 07 15 18 automatic transmission7 B black7 and C white a Obtain PA7 PB b Obtain PA O B c Obtain PAlB d Obtain PAlC An oil exploration company currently has two active projects7 one in Asia and the other in Europe Let A be the event that the Asian project is successful and B be the event that the European project is successful Suppose that A and B are independent events with PA 4 and PB 7 a If the Asian project is not successful7 what is the probability7 that the European project is also not successful STT 351 HW on Ch 1 hra Jan 19 Thursday 01 Questions 1 The accompanying data are speci c gravity values for various wood types used in construction 31V35V36V37V41V41V42V42V45v46v46v48v54v55v6 Obtain the following by hand using calculator not Matlab a size of the sample b Sample mean Y and sample median c Sample variance 827 sample standard deviation S d 1st7 2nd and 3rd sample quartile e histogram of the data f Box plot of the data Do we have outliers STT 351 HW on Ch 3 Due Feb 8 Wed Questions 1 Let X be a discrete random variable with VX 86 then V3X56 is P Let X be a discrete random variable with EX2 1975 and VX 163 then EX 9 lf random variable X has distribution Bin 1075 VX is r If random variable X has distribution Bin 1075 PX 3 is 9 If the expected value of a discrete random variable X is EX 5 then E2X 3 is 03 The probability mass function of a discrete random variable X is de ned as p xlO for z 01234 Then the value of the cumulative distribution function at z 3 is 5 If random variable X has distribution Bin6 3 EX is 00 The mean of the hypergeometric random variable X with parameters 7110 M 50 and N 100 is p The cumulative distribution function of a discrete random variable X is F1 4 F2 7 F3 9 and F4 1 then the value of the probability mass function p at X 3 is 10 The expected value of the negative binomial random variable X with parameters 7 5 and p 8 is 11 The prnf for X the number of major defects on a randomly selected gas stove of a certain type is c The standard deviation of X 12 Suppose that only 25 of all drivers come to a complete stop at an intersection hav ing ashing red lights in all directions when no other cars are visible What is the probability that7 of 20 randomly chosen drivers coming to an intersection under these conditions7 a At most 6 will come to a complete stop b Exactly 6 will come to a complete stop c At least 6 will come to a complete stop d What is the expectation value for number of drives coming to a complete stop from next 20 drivers 13 Use appendix A1 or Matlab to obtain the following a 13457 3 b b415 3 e P2 X g 4 when X m Bin10 3 d PX lt 4 when X N Bin10 3 e PX 2 3 when X N Bin107 3 f P3 lt X lt 5 when X N Bin107 3 14 The re department is concerned that many homes remain without detectors Let p the true proportion of such houses having detectors The re department will take random sample of 25 homes7 and if less than 15 of the sampled homes are using the smoke detector7 then the department will inspect each home in the entire district a lfp 807 what is Pinspection takes place b lfp 707 what is Pinspection takes place c If we change the cut line of 15 to 147 how does the probability in previous two questions will change 15 The number of people arriving for treatment at an emergency room can be modeled by a Poisson process with a rate parameter of ve per hour a What is the probability that exactly four arrivals occur during a particular hour b What is the probability that at least four people arrive during a particular hour 16 There are 5 red balls and 3 blue balls in a box 3 balls are drawn from the box at once If at least 1 blue ball is drawn7 the draw is marked as success Let X denote the number of successful draws after 6 draws What is the distrubution of X7 17 There are 20 steel manufacturer in the city7 and 6 of them is actually Violating the city7s enViromental protection law You are going to randomly select 10 manufacturer in the city and and inspect them Let X be the number of Violating manufacturer caught in Violation a What is the distribution function of X b What is the probability7 that all of 6 Violators will be caught

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