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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 off 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 first defective car is the 100th car to roll off the production line that day? 2. What is the chance that the first defective car is not among the first 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) . ²ix λ > 0. The probability mass function of a random variable X is given by p ( { i } ) = c λ 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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