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