5.2 Any lower Lebesgue-Darboux sum does not exceed any upper Lebesgue-Darboux sum i.e. for any two partitions P₁ and P₂ L(f, P₁) ≤ U(f, P₂) and L(f. P₂) ≤ U(f, P₁)
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- Suppose that 2 balls are randomly selected (without replacement) from an urn containing 3 red, 4 blue, and 5 white balls. If we let X and Y denote, respectively, the number of red and white balls chosen. Solve for P(X=2).Consider two points (x0, y0) and (x1, y1). Prove that the first order Langrange polynonial is equivalent to linear interpolation.Let X be the amount of soda released by a soft-drink dispending machine into a 6-ounce cup. Assume that X is normally distrubuted with o = .25 ounces and that the average "fill" can be set by the vendor. (1) At what quantity should the average "fill" be set so that no more than .5% of the releases overflow the cup? (2) Using the average "fill" found in part (a), determine the minimal amount that will be dispensed in 99% of the cases.
- 1. Let x be the number of red balls among 3 balls randomly selected from a bag containing 9 black ball and 6 red P(x=0) P(x=1)they take samples of 4 fireworks for quality co from and examine them for defects. let X be the number of defective fireworks in the sample of 4.Suppose that 2 balls are randomly selected (without replacement) from an urn containing 3 red, 4 blue, and 5 white balls. If we let X and Y denote, respectively, the number of red and white balls chosen. a) Solve for P(x=0, y=0) b)Solve for P(x=1, y=2) c)Solve for P(x=2, y=1)
- (X1,X2,...,Xn) are iid, Xi ∼N(μ,σ2). Compute Var(S2).#8 found z already what is w?Calculate the coefficient of x7y5zx7y5z in (x+y+z)13(x+y+z)13. (b) In her discrete math class, Karen was asked to count the number of four-person teams that could be formed from a group of 17 males and 13 females with at least one male and at least one female. They mistakenly argue as follows: There are 17 choices for a male on the team and 13 choices for a female on the team. After that, there are (282)(282) to choose the remaining two players from the remaining 28 individuals. Therefore, by the rule of product, there are 17⋅13⋅ (28⋅27)/2 different teams. i. Explain the error in Karen's reasoning. ii. Determine the correct number of four-person teams that can be formed with at least one male and at least one female. (You may leave your answer in terms of unsimplified binomial coefficients.)
- In a bag of 340 chocolate candies, 35 of them are brown. The candy company claims that 13% of its plain choclate candies are brown. For following assume that the claim of 13% is true and assume that a sample conists of 340 chocolate candies. Complete a-e A) for the 340 choclate candies use the range rule of thumb to identify the limits separating numbers of brown choclate candies that are significantly low and those that r high values of _ brown cadies or fewer are low B) values of _ brown cadies are higher C) Find the probabilityA company sells candy in jars that each have a volume of 3 cups. Each jar is filled above a certain line, guaranteeing that it has more than 3/8 cups of candy. In which of the following does the shaded region represent the possible volumes of candy, c, in cups, a customer may have, given that they bought j jars of candy?The manufacturer of large liquid crystal display (LCD) is difficult. Some defectsare minor and can be removed; others are unremovable. The number of unremovabledefects for each of n = 45 displays1 0 5 3 0 7 6 0 0 4 6 85 0 9 1 0 8 6 0 3 2 0 00 6 0 10 0 6 0 0 1 0 0 00 1 5 1 0 5 0 0 2has mean ̅ x= 2.667 and s = 3.057 unremovable defects. Conduct a test of hypothesis withthe intent of showing that the mean number of unremovable defects is less than 3.6. Take α= 0.025.
