Handout6 - to be inspected 3. Do the same problem if the...

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STOR 435 Handout 6 Sections 4.1-4.3 These are examples that we will do when trying to understand Chapter 4. Example 1 (Discrete random variables) . A coin has P ( H ) = 2 / 3 , P ( T ) = 1 / 3 You toss the coin twice. Let X be the number of heads you observe. Calculate the probabilities for the various values X could take. Example 2 (Example 1b from book) . You have a box with 20 tickets labelled 1 , 2 , . . ., 20. You pick 3 tickets without replacement. You will win a prize if one of the tickets is at least 19 or higher. What is the chance of you winning? Example 3 (Discrete random variable) . 1. An engineer working in car factory inspects each car as it comes out of the inspection line. Assume that each car coming oF the inspection has probability %.01 of having a defect, independent of any other car. The engineer comes into work and starts inspecting cars one by one. What is the chance that the ±rst defective car is the 100th car to roll oF the production line that day? 2. What is the chance that the ±rst defective car is not among the ±rst 20
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Unformatted text preview: to be inspected 3. Do the same problem if the probability of a defect is not . 01 but some value p and now do it not for the 100th car but for a general k 1. Example 4 (Example 2a, pmf) . ix > 0. The probability mass function of a random variable X is given by p ( { i } ) = c i i ! for i and p ( x ) = 0 otherwise, where c is an appropriately chosen constant. What is c ? What is P ( X = 4)? Example 5 (Cumulative distribution function) . Draw the cumulative distribu-tion function of the random variable X in the rst example (# of heads in two tosses of a coin). Example 6 (Cumulative distribution function) . 4.19 Example 7 (Expected value) . 1 1. Find expected value of the random variable X in example 1. 2. You are tossing a fair dice. Let X be the face you observe. Find E ( X ). 3. 4.25 4. 4.13: Let X denote the sales of the salesperson. Find E ( X ). Suggested extra problems: Self test problems 4.1, 4.2 2...
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This note was uploaded on 05/11/2011 for the course STOR 435 taught by Professor Shakar during the Spring '11 term at University of North Carolina School of the Arts.

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Handout6 - to be inspected 3. Do the same problem if the...

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