10C_REVIEW - Math 10C Final Exam Review Outline Basic...

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1 Math 10C Final Exam Review Outline Basic Information for the Final Exam: The exam will consist of approximately 8 questions, with multiple parts . You will not be allowed a calculator on the exam, so please do not bring one. You should bring a number two pencil. (You can bring more than one if you feel so inclined.) You are not permitted a page of notes, but a reference sheet with relevant formulas will be provided on the exam. Also bring your student ID card , as we will be checking those at the exam. We reserve the right to place your backpacks in the front of the class. Also, don’t worry about bringing a blue book, as you will be able to write directly on the exam. The exam will be held Tuesday, June 12 th , 2007 from 3:00 – 6:00pm , in Peterson 110 . The test is designed to take about two hours. This means that you should have sufficient time to go back through your work and check your math. Remember, does your answer make sense? (Draw a picture/plug numbers in.) Do not cheat on this exam. Cheating will be taken seriously and you will fail the course . So, please do not cheat. Also, solutions will be posted on my website http://math.ucsd.edu/~wgarner/math10c/ some time after the exam so you can get a rough idea how you did. Finally, grades should be posted on Tritonlink around June 21 st .
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Math 10C Final Exam Review Outline 2 2b t 3c P H x L t p H L Section 8.7: Distribution Functions Know the def of a probability density function (pdf) and how to compute a probabilities - ex. After conducting extensive research, the American Automobile Association has discovered that the length of time between tune-ups for minivans is a continuous random variable T , measured in years, and that the probability density function for T is 1 /3 9 0i f 0 if 0 () T T Te T fT < = . What is the probability that a minivan will be driven between one and two years between tune-ups? Know the definition of a cumulative density function (c.d.f.) Know what each looks like and their respective properties Know how to tell the differences between a p.d.f. and a c.d.f. - ex. The graphs of the cdf, P ( x ) and pdf, p ( x ) are shown below. Using the properties of a cdf, find the value of c . Using the properties of a pdf, find b . Note: Suppose p ( t ) is the density function for ages in a population, where t is measured in years. p (23) = 0.4. This is not telling us that 40% of the population is precisely age 23. Rather, p (23) = 0.4 does tell us that for some small interval D t around 23, the fraction of the population with ages in this interval is approximately p (23) D t = 0.4 D t . Section 8.8: Probability, Mean, and Median Know the definition of mean and median - The mean is xpxdx −∞ and the median is the value T such that 0.5 ( ) T pxdx −∞ = Know how to find the mean/median given a distribution function - ex. Suppose x measures the time (in seconds) that you wait for the red light to turn green. The p.d.f. for x is given by 1 40 if 0 40 0o t h e r w i s e x px ≤ ≤ = . What is the probability that you will wait at least 15 seconds for the red light to turn green? What is the median wait time for the red light to turn green? What is
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10C_REVIEW - Math 10C Final Exam Review Outline Basic...

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