Study guide for exam 1
Study guide for exam 1 ENGR 0020: Probability and statistics for Engineers I
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This 6 page Study Guide was uploaded by Emily Binakonsky on Sunday February 8, 2015. The Study Guide belongs to ENGR 0020: Probability and statistics for Engineers I at University of Pittsburgh taught by Maryam Mofrad in Spring2015. Since its upload, it has received 638 views. For similar materials see Probability and Statistics for Engineers 1 in Engineering and Tech at University of Pittsburgh.
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Date Created: 02/08/15
Study Guide for Exam 1 Emily Binakonsky Introduction and Descriptive Statistics 1 Find the sample mean sample median and sample standard deviation of the following data Use correct mathematical notation and show all steps 15 32 27 20 16 28 26 21 19 25 31 23 29 30 22 24 21 27 18 19 17 22 23 16 2 Construct a StemandLeaf plot of the data above Then construct and appropriately label a box plot of the data as well Which plot displays data most appropriately Probability 3 A water testing facility utilizes two different devices to extract harmful particles out of runoff water and then reintroduce the decontaminated water back to waterways The first device is used 70 of the time The second device is used 30 of the time The known probability of error in device one s decontamination is 02 while the known probability of error in two s decontamination is 04 Suppose an error occurred in the decontamination of the treated water What device would you guess decontaminated the treated water Show all steps and explain your answer 4 You are playing a poker hand of 5 cards Find the probability of holding 2 kings and 3 aces Show all work What rules and or theorems did you use Study Guide for Exam 1 Emily Binakonsky 5 A box contains a1000 manila envelopes full of bara bonds Of those 1000 envelopes 750 contain 1000 in bara bonds 125 contain 750 in bara bonds 75 contain 300 in bara bonds and 50 contain 100 in bara bonds A manila envelope costs 75 Draw a tree diagram What is the sample space of the different amounts of bara bonds Assign probabilities to the sample points Find the probability that the first purchased envelope contains less than a 1000 6 The probability that a doctor correctly diagnoses a patient s particular illness and that patient recovers from that illness is 6 Given the doctor makes an incorrect diagnosis the probability that the patient dies is 7 Find the probability that a doctor makes an incorrect diagnosis and the patient dies What theorem and rule did you use 7 The probabilities that a teaching assistant will assign grades A B C D or E to students term papers in a twohour period are 020 023 028 015 and 14 respectively Find the probability that in this twohour period that a That a grade of a C or better is assigned b That a grade of at least a B is assigned c That a grade higher than a D is assigned Study Guide for Exam 1 Random Variables and Probability Distributions Emily Binakonsky 8 What is the concept of a random variable Provide an example 9 What is a probability distribution discrete and continuous What are the three conditions that must be met Provide an example of a discrete and continuous random variable X 10 What is a Cumulative Distribution Function Fx 11 What is a probability density function pdf What are the three conditions that must be met for it to be a pdf for the discrete random variable The continuous random variable 12 An investment firm offers its customers bonds that mature after varying number of years Given that the cumulative distribution of S the number of years to maturity for a randomly selected bondB Q 25 PS 50 75 10 a Find PS 5 b Find PS gt 3 c Find P14 lt S lt 6 d Find PS s 5s 2 2 slt1 lsslt3 BSslt5 SSSlt7 27 Study Guide for Exam 1 Emily Binakonsky 13 An important factor in ice cream is the air bubble size distribution Significant problems occur if the air bubbles sizes are too large From production data in the past it has been determined that the air bubble size in micrometers distribution is characterized by 3x394 x gt 1 fx 0 otherwise a Verify that this is a valid density function Evaluate Fx c What is the probability that a random air bubble from the manufactured ice cream exceeds 5 micrometers Show work 14 A fastfood joint operates a drivethrough facility and a walkin facility On a randomly selected day let X the proportion of time that the drivethrough facility operates and let ythe proportion of time the walkin facility operates Suppose the joint density function of these random variable is 2 fxy xy OSxSlOSySl 0 otherwise a Find the joint probability distribution of X and Y b PxyE A where A is the region that is given by xy xy S 2 Study Guide for Exam 1 Mathematical Expectation Emily Binakonsky 15 From the textbook410 Two tirequality experts examine stacks of tires and assign a quality rating to each tire on a 3point scale Let X denote the rating given by expert A and Y denote the rating given by B The following table gives the joint distribution for X and Y v fxv 1 2 3 1 010 005 002 x 2 010 035 005 3 003 010 020 Find x and My 16 Given a random variable X with standard deviation ox and a random variable Y a bX show that if b lt 0 the correlation coef cient pXY 1 and if b gt O on 1 Study Guide for Exam 1 Emily Binakonsky 17 If a random variable X is de ned such that EX 12 10 and EX 22 6 find it and 02
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