A. Suppose 5 balls are selected from an urn containing 1 red ball, 1 blue ball, and I green ball usingsimple random sampling with replacement.Define 22= {(01,02,003,004,005): 0; = color of the selected ball = {R,G,B),i=1,2,....5}(For example: (R,G,R,B,G) represents the outcome where the 1st and 3rd ballsselected are red, 2nd and 5th balls are green while the 4th ball is blue)G₁ = set of elements of where the ith selected ball is green, i=1,2,...,5B₁ = set of elements of where the ith selected ball is blue, i=1,2,...,5Express the following sets as a composition of the Gis and Bis:1. A =set containing elements of 2 where the 2nd and 3rd balls selected are blue2. B =set containing elements of 2 where the first 4 balls selected are blue, while the last ball is redset containing elements of 2 where there is at least one blue ball selected3. C =4. D=set containing elements of 2 where there are exactly 4 blue balls5. E= set containing elements of 2 where all the balls selected are red

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Answered: A. Suppose 5 balls are selected from an…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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23 A bag contains a white and b black balls. Balls are chosen from the bag according to the following method: A. A ball is chosen at random and is discarded. B. A second ball is then chosen. If its color is different from that of the preceding ball, it is replaced in the bag and the process is repeated from the beginning. If its color is the same, it is discarded and we start from step 2. In other words, balls are sampled and discarded until a change in color occurs, at which point the last ball is returned to the urn and the process starts anew. Let Pa,b denote the probability that the last ball in the bag is white. Prove that Hint: Use induction on k = a + b. Pa,b - 1 2
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Suppose there are three balls in a box. On one of the balls is the number 1, on another is the number 2, and on the third is the number 3. You select two balls at random and without replacement from the box and note the two numbers observed. The sample space S consists of the three equally likely outcomes {(1, 2), (1, 3), (2, 3)} (disregarding order). Let X be the sum of the two balls selected. Which of the following is the correct distribution for X?
A sample of 3 balls is to be selected at random from an urn containing 20 balls numbered 1 to 20. Six balls are green, 4 balls are white, and 10 balls are black. How many different samples can be selected?
Q7
Q1) Below find the records of 12 randomly selected used pickup trucks (none used commercially) and 11 randomly selected used passenger cars, the time (in years) that they were kept by the original owner before being sold: Used pickup trucks | 3 | 2.5 2.9 5 4.2 3.1 3.3 4 5.3 3.8 4.5 Used passenger cars | 2.2 3 2.8 4.3 4 3.3 2.9 2.1 2 3.1 3 It is known that the standard deviation of used pickup trucks is 2 years and of used passenger cars is 1 year. (a) Investigate, at the 5% significant level, whether the mean time (in years) that used pickup trucks were kept by the original owner before sold is larger than used passenger cars. (b) What assumption is needed to perform the test in (a). (c) Construct the 96% confidence interval for the mean difference of time (in years) were kept by the original owner before sold between used passenger cars and used pickup trucks. Use this confidence interval to tell whether there is difference in the mean time (in years) between these 2 tynes of…
Many manufacturers have quality control programs that include inspection of incoming materials for defects. Suppose a computer manufacturer receives computer boards in lots of five. Three boards are selected from each lot randomly for inspection. If we number the boards 1, 2, 3, 4, and 5, a possible random selection is (2, 4, 5). a. List the ten different possible selections. b. Suppose that the boards 1 and 4 are the only defective boards in a lot of five. Three boards are to be chosen at random. Define X as the number of defective boards observed among those inspected. Find the probability distribution (pmf) of X.
2. 1 to your empo prvi na Burner 1 3 We have three pancakes. One is burnt on two sides, one on one side, and one not at all. The pancakes are stacked on a plate in such a way that all that can be seen is a burnt side on top. How likely is it that the fully burnt pancake is the one on top? Alhaal han the number and 1 through 26 arranged randomly across its 38 clat + 1/2 D + E (1 3 N
In a survey, it was found that 80% of adults operate the flusher of toilets in public restrooms with their foot. (a) If 300 adults are randomly selected, how many would we expect to flush toilets in public restrooms with their foot? (b) Would it be unusual to observe 255 adults who flush toilets in public restrooms with their foot? (a) We would expect (Type a whole number.) adults to flush toilets in public restrooms with their foot. (b) Would it be unusual to observe 255 adults who flush toilets in public restrooms with their foot? Choose the correct answer below. O A. Yes, because 255 is greater than u + 2o. O B. No, because 255 is greater than u + 20. O C. Yes, because 255 is between u - 20 and u+ 20. O D. No, because 255 is less than u- 20. O E. No, because 255 is between u -20 and u+ 20.
Suppose that you have 10 cards. 3 are blue and 7 are orange. The 3 blue cards are numbered 1,2, and 3. The 7 orange cards are numbered 1, 2, 3, 4, 5, 6, and 7. The cards are well shuffled. You randomly draw one card. • B = card drawn is blue • O = card drawn is odd-numbered How many elements are there in the sample space? [ Select ] ["7", "10", "2", "3"] P(B) = [ Select ] ["0.7", "0.2", "0.5", "0.3"](Give your answer in decimal form.
What is your favorite color? A large survey of countries, including the United States, China, Russia, France, Turkey, Kenya, and others, indicated that most people prefer the color blue. In fact, about 24% of the population claim blue as their favorite color.t Suppose a random sample of n = 59 college students were surveyed and r = 8 of them said that blue is their favorite color. Does this information imply that the color preference of all college students is different (either way) from that of the general population? Use a = 0.05. A USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Ho: p = 0.24; H,: p + 0.24 O Họ: p = 0.24; H: p 0.24 (b) What sampling distribution will you use? O The standard normal, since np > 5 and ng > 5. The standard normal, since np 5 and ng > 5. The Student's t, since np < 5 and ng < 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find the P-value of the test statistic.…

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