Mathematics for Elementary Teachers with Activities (5th Edition)
5th Edition
ISBN: 9780134392790
Author: Beckmann, Sybilla
Publisher: PEARSON
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Chapter 11.2, Problem 5P
The Lazy Daze Pool Club and the Slumber-N-Sunshine Pool Club have a friendly rivalry going. Each club claims to have the bigger swimming pool. Make up realistic sizes for the clubs’ swimming pools so that each "club has a legitimate basis for saying that it has the larger pool. Explain clearly why each club can say its pool is biggest. Be sure to use appropriate units. Considering the function of a pool, what is a good way to compare sizes of pools? Explain.
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6. Show that
1{AU B} = max{1{A}, I{B}} = I{A} + I{B} - I{A} I{B};
I{AB} = min{I{A}, I{B}} = I{A} I{B};
I{A A B} = I{A} + I{B}-21{A} I {B} = (I{A} - I{B})².
Theorem 3.5 Suppose that P and Q are probability measures defined on the same
probability space (2, F), and that F is generated by a л-system A. If P(A) = Q(A)
for all A = A, then P = Q, i.e., P(A) = Q(A) for all A = F.
6. Show that, for any random variable, X, and a > 0,
Lo P(x
-00
P(x < x
Chapter 11 Solutions
Mathematics for Elementary Teachers with Activities (5th Edition)
Ch. 11.1 - For each of the following metric units, give...Ch. 11.1 - For each of the following items, state which U.S....Ch. 11.1 - What does it mean to say that a shape has an area...Ch. 11.1 - Discuss why it is easy to give an incorrect...Ch. 11.1 - Discuss: Why is it not completely correct to...Ch. 11.1 - Describe how it could happen that three different...Ch. 11.1 - Pick two ideas or concepts from your reading of...Ch. 11.1 - Visit a store and write down at least 10 different...Ch. 11.2 - Describe one-dimensional, two-dimensional, and...Ch. 11.2 - Describe one-dimensional, two-dimensional, and...
Ch. 11.2 - Drawing on your reading from this section,...Ch. 11.2 - Describe one-dlmenslonal, two-dlmenslonal, and...Ch. 11.2 - The Lazy Daze Pool Club and the Slumber-N-Sunshine...Ch. 11.2 - Suppose there are 2 rectangular pools: One is 30...Ch. 11.2 - Minh says that the rectangle on the left in Flgure...Ch. 11.3 - One source says that the average distance from the...Ch. 11.3 - If an object is described as weighing 6.20 grams,...Ch. 11.3 - Tyra ls calculating the distance from town A to...Ch. 11.3 - John has a paper square that he believes is 100 cm...Ch. 11.3 - Sally has a Plexiglas cube that she believes is...Ch. 11.4 - A recipe calls tor 4 ounces ot chocolate. If you...Ch. 11.4 - A class needs 27 pieces of ribbon, each piece 2...Ch. 11.4 - To convert 24 yards to feet, should you multiply...Ch. 11.4 - To convert 2000 kilometers to meters, should you...Ch. 11.4 - Shauntay used identical plastic bears to measure...Ch. 11.4 - A car is 16 feet, 3 inches long. How long is it in...Ch. 11.4 - The distance between two cities is described as...Ch. 11.4 - In Germany, people often drive 130 kilometers per...Ch. 11.4 - One foot is 12 inches. Does this mean that 1...Ch. 11.4 - A room has a floor area of 48 square yards. What...Ch. 11.4 - One kilometer is 1000 meters. Does this mean that...Ch. 11.4 - One foot is 12 inches. Does this mean that 1 cubic...Ch. 11.4 - How much mulch will you need to cover a...Ch. 11.4 - A classroom has a floor area of 600 square feet....Ch. 11.4 - A house has a floor area of 800 square meters....Ch. 11.4 - A house has a floor area of 250 square meters....Ch. 11.4 - The Smiths will be carpeting a room in their...Ch. 11.4 - One acre is 43,560 square feet. If a square piece...Ch. 11.4 - A construction company has dump trucks that hold...Ch. 11.4 - The following questlon explores why It doesn’t...Ch. 11.4 - A penny is 116 of an inch thick. Suppose you have...Ch. 11.4 - Write 100 zeros on a piece of paper and time how...Ch. 11.4 - For a certain type of rice, about 50 grains till a...Ch. 11.4 - Assuming that 1 gram of gold is worth $30 how much...Ch. 11.4 - Imagine that all the people on earth could stand...Ch. 11.4 - Joey has a toy car that is a 1: 64 scale model of...
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- Don't use ai to answer I will report you answerarrow_forward5. Suppose that X is an integer valued random variable, and let mЄ N. Show that 8 11118 P(narrow_forward食食假 6. Show that I(AUB) = max{1{A}, I{B}} = I{A} + I{B} - I{A} I{B}; I(AB)= min{I{A}, I{B}} = I{A} I{B}; I{A A B} = I{A} + I{B}-21{A} I{B} = (I{A} - I{B})². -arrow_forward11. Suppose that the events (An, n ≥ 1) are independent. Show that the inclusion- exclusion formula reduces to P(UAL)-1-(1-P(Ak)). k=1 k=1arrow_forward8. Show that, if {Xn, n≥ 1} are independent random variables, then sup X,, A) < ∞ for some A.arrow_forward20. Define the o-field R2. Explain its relation to the o-field R.arrow_forward11. (a) Define the (mathematical and conceptual) definition of conditional probability P(A|B).arrow_forward12. (a) Explain tail events and the tail o-field. Give an example.arrow_forwardLet A, A1, A2,... be measurable sets. Then P(A)=1- P(A); • P(Ø) = 0; P(A1 UA2) ≤ P(A1) + P(A2); A1 C A2 P(A1) P(A2); P(UA) + P(n=14) = 1. Exercise 3.1 Prove these relations. ☐arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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