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# (a) Solve the system (b) Find the solution that satisfies the initial conditions , ,

ISBN: 9780470432051 396

## Solution for problem 3 Chapter 5.4

Elementary Linear Algebra: Applications Version | 10th Edition

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Elementary Linear Algebra: Applications Version | 10th Edition

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Problem 3

(a) Solve the system (b) Find the solution that satisfies the initial conditions , , .

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Stat notes 9/21 nPr= n place r ­ Use when the order of something is important and relevant. nCr= n choose r ­ Use when the order of something is irrelevant, but the overall result is relevant. 1.) A bag contains 10 colored balls, 5 red and 5 green. If you draw 3 without replacement, what is the probability that all three are green ­ Order does not matter here so we’ll be using nCr ­ 10C3 ways to draw 3 general balls out of the 10 ­ 5C3 to draw 3 green balls from the bag ­ Poob(3 green balls)= 5C3/10C3= (5x4x3/3x2x1)/(10x9x8/3x2x1)= 1/12 ­ C means n(n­1)(n­2)... (n­r) 2.) You have 10 cards numbered 1­10. After shuffling, you place 3 in a row. What is the probability of getting 3 in increasing sequence. ­ Order matters here so we’ll be using nPr ­ 10P3 ways to place 3 out of 10 in sequence ­ 8 ways to draw 3 of 10 in increasing sequence ­ (1,2,3)(2,3,4)(3,4,5)(4,5,6)(5,6,7)(6,7,8)(7,8,9)(8,9,10) ­ (8/720)­(4/360)= 1/90 Discrete vs continuous random variables ­ Look at sample space ­ Discrete or continuous If discrete, then random variable is discrete; if continuous, then random variable is continuous. ­ Sample space is a set of numbers ­ A continuous set (sample size) is composed of intervals ­ A

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(a) Solve the system (b) Find the solution that satisfies the initial conditions , ,