Theorem 22.1. Suppose that n people (n 2 2) are at a party. Then there exist at least two people ...
-11 points BBUnderStat12 1.2.016. O Ask Your T Suppose there are 30 people at a party. Do you think any two share the same birthday? Let's use the random-number table to simulate the birthdays of the 30 people at the party Ignoring leap year, let's assume that the year has 365 days. Number the days, with 1 representing January 1, 2 representing January 2, and so forth, with 365 representing December 31. Draw a random sample of 30 days (with...
F1. need help solving this problem. 1. (25 pts) Here's a neat theorem. Suppose that f la, b] [a, b] is continuous; then f will always map some s-value to itself (a so-called fixed point): i.e. 3 c E (a, b) for which f(c)-c (a) Give a "visual proof" of this theorem. Hint: take your inspiration from our "visual proofs" of Theorem 15 and IVT And notice here that the domain and range of f are the same interval; this...
5.36. (a) In a group of 23 strangers, what is the probability that at least two of bout if there are 40 strangers? In a group them have the same birthday? How a of 200 strangers, what is the probability that one of them has the same birthday as your birthday? (Hint. See the discussion in Sect. 5.4.1.) (b) Suppose that there are N days in a year (where N could be any number) and that there are n people....
Suppose there are 100 zero-coupon bonds with the same maturity (duration), issued by 100 private corporations. I want you to consider how the average yield on the bonds will change from Monday to Tuesday as described below. (The average yield on these 100 bonds is the number you get by adding up all the 100 yields and dividing by 100). On Monday, everyone knows that 50 of these corporations will be bankrupt before the bonds are due. But no one...
Suppose you are organizing a party for a large group of your friends. Your friends are pretty opinionated, though, and you don’t want to invite two friends if they don’t like each other. So you have asked each of your friends to give you an “enemies” list, which identifies all the other people among your friends that they dislike and for whom they know the feeling is mutual. Your goal is to invite the largest set of friends possible such...
2,6,7 help Points: 3 225 23320 Score: (3 pts. (2 pts.] 2 pts. 1. Copy Theorem 17.8 and its proof from your textbook (see pages 93-94). Attempt to understand how all parts of the proof come together. C h rial Formula 2. A coin is tossed twelve times. How many sequences with 6 heads and 6 tails are possible? 3. (Page 89, Exercise 16.9) You wish to make a necklace with 20 different beads. In how many different ways can...
3.11 Theorem. Suppose f(x)-a"x" + an-lx"-+ + ao is a poly- nomial of degree n > 0 and suppose an > 0. Then there is an integer k such that ifx >k, then f(x)> 0. Note: We are only assuming that the leading coefficient an is greater than zero. The other coefficients may be positive or negative or zero. The next theorem extends the idea that polynomials get positive and roughly states that not only do they get positive, but...
using these axioms prove proof number 5 1 - . Axiom 1: There exist at least one point and at least one line Axiom 2: Given any two distinct points, there is exactly one line incident with both points Axiom 3: Not all points are on the same line. Axiom 4: Given a line and a point not on/ there exists exactly one linem containing Pouch that / is parallel tom Theorem 1: If two distinct lines are not parallet,...
Please do exercise 129: Exercise 128: Define r:N + N by r(n) = next(next(n)). Let f:N → N be the unique function that satisfies f(0) = 2 and f(next(n)) =r(f(n)) for all n E N. 102 1. Prove that f(3) = 8. 2. Prove that 2 <f(n) for all n E N. Exercise 129: Define r and f as in Exercise 128. Assume that x + y. Define r' = {(x,y),(y,x)}. Let g:N + {x,y} be the unique function that...
5. Three boxes are numbered 1, 2 and 3. For k 1, 2, 3, box k contains k blue marbles and 5 - k red marbles. In a two-step experiment, a box is selected and 2 marbles are drawn from it without replacement. If the probability of selecting box k is proportional to k, then the probability that two marbles drawn have different colours is 6. Two balls are.dropped in such a way that each ball is equally likely to...