Chapters 5-7 - ShareStudies.com
... Wing Foot is a shoe franchise commonly found in shopping centers across the U.S. Wing Foot knows that its stores will not show a profit unless they make over $540,000 per year. Let A be the event that a new Wing Foot store makes over $540,000 its first year. Let B be the event that a store makes mo ...
... Wing Foot is a shoe franchise commonly found in shopping centers across the U.S. Wing Foot knows that its stores will not show a profit unless they make over $540,000 per year. Let A be the event that a new Wing Foot store makes over $540,000 its first year. Let B be the event that a store makes mo ...
Expected Uses of Probability
... Let n and k be integers with n ≤ 2k/2 and k ≥ 3. Then it is possible to color the edges of the complete graph on n vertices with the following property: one cannot find k vertices for which the k2 edges among them are monochromatic. Remark. In the language of Ramsey numbers, prove that R(k, k) > 2k ...
... Let n and k be integers with n ≤ 2k/2 and k ≥ 3. Then it is possible to color the edges of the complete graph on n vertices with the following property: one cannot find k vertices for which the k2 edges among them are monochromatic. Remark. In the language of Ramsey numbers, prove that R(k, k) > 2k ...
Class Notes MAE 301 10/8/09 Greatest Common Divisor (GCD
... therefore sin(x) is not injective. To properly define sin-1 we must first restrict the domain of f(x) to -π/2 < x < π/2 so that sin(x) is injective, and therefore invertible, over that segment. In layman terms if sin(some x) = .8 then sin-1 would equal the angle x whose sin is .8. It must be noted, ...
... therefore sin(x) is not injective. To properly define sin-1 we must first restrict the domain of f(x) to -π/2 < x < π/2 so that sin(x) is injective, and therefore invertible, over that segment. In layman terms if sin(some x) = .8 then sin-1 would equal the angle x whose sin is .8. It must be noted, ...
Basic Probability Rules
... the other hand, probabilities are numbers. More specifically, they are numbers between 0 and 1 (including those extremes). Thus, it is legitimate to add, multiply, and divide probabilities but not to take complements, intersections, or unions of them. The “at random” selection implies that each of t ...
... the other hand, probabilities are numbers. More specifically, they are numbers between 0 and 1 (including those extremes). Thus, it is legitimate to add, multiply, and divide probabilities but not to take complements, intersections, or unions of them. The “at random” selection implies that each of t ...
Solutions to homework 1
... which either option 1 or 2 occurs. Any i ∈ A will have come from case 1 meaning that i ∈ B, so A ⊆ B as required. As such the number of pairs A, B with the desired properties is indeed 3n . Problem 60. I assume we are choosing an order (e.g. 3 bagels of type 1, 0 bagels of type 2, . . . ) at random ...
... which either option 1 or 2 occurs. Any i ∈ A will have come from case 1 meaning that i ∈ B, so A ⊆ B as required. As such the number of pairs A, B with the desired properties is indeed 3n . Problem 60. I assume we are choosing an order (e.g. 3 bagels of type 1, 0 bagels of type 2, . . . ) at random ...
sol - probability.ca
... (c) [3] Provide an estimate of P (Y > 100). [Hint: if a value is too large for the standard normal table, then what can you conclude?] Solution. Again Z = (Y − 20)/4 has the standard normal distribution, so P (Y > 100) = P ((Y − 20)/4 > (100 − 20)/4) = P (Z > 20) = 1 − P (Z < 20). Now, the table onl ...
... (c) [3] Provide an estimate of P (Y > 100). [Hint: if a value is too large for the standard normal table, then what can you conclude?] Solution. Again Z = (Y − 20)/4 has the standard normal distribution, so P (Y > 100) = P ((Y − 20)/4 > (100 − 20)/4) = P (Z > 20) = 1 − P (Z < 20). Now, the table onl ...
Discrete Probability Distribution / Expectations
... Discrete Probability Distribution / Expectations 1. A coin is biased so that a head is three times al likely to occur as a tail. Find the expected number of tails when this coin is tossed twice. Ans: ...
... Discrete Probability Distribution / Expectations 1. A coin is biased so that a head is three times al likely to occur as a tail. Find the expected number of tails when this coin is tossed twice. Ans: ...