Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable, X for the right tire and Y for the left tire, with joint pdfF(x, y) = { K (x² + y²)20 ≤ ≤ 30, 20 ≤ y ≤ 30otherwise(a) What is the value of K? (Enter your answer as a fraction.)K=(b) What is the probability that both tires are underfilled? (Round your answer to four decimal places.)(c) What is the probability that the difference in air pressure between the two tires is at most 2 psi? (Round your answer to four decimal places.)(d) Determine the (marginal) distribution of air pressure in the right tire alone.for 20≤x≤ 30(e) Are X and Y independent rv's?Oves, f(x, y) = fx(z) - fy (y), so X and Y are independent.Oves, f(x, y) + fx(z) - fy(y), so X and Y are independent.ONO, f(x, y) = fx(2) - fy(y), so X and Y are not independent.ONO, f(z,y) #fx(z) - fy(y), so X and Y are not independent.

Each front tire on a particular type of vehicle is supposed to be filled with a pressure of . is the…

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The Statistical Abstract of the United States reported that 66% of students who graduated from high school in 2012 enrolled in college. Let X be the number of high school students that enrolled in college. Formulas needed: E (X) = n * p and Var (X) = n * p * (1 − p) - a) If exactly 18 high school students are chosen at random, the expected number of high school students are enrolle in college is Round your answer to next whole number. b) If exactly 18 high school students are chosen at random, the std(X), standard deviation of the number of them that are enrolled in college is Round your answer to the nearest whole number.
In a survey of 1150 adult males, 805 said they use the Internet. In a survey of 1050 females, 746 said they use the Internet. At α= 0.05, can you reject the claim that the proportion of Internet users are the same for both groups?
A survey asked 500 random people how often they use the bathroom on a daily basis. Nineteen percent of respondents said they used the bathroom just once daily, 25% twice daily, 39% three times daily, 12% four times daily, 3% five times daily, and 2% six times daily. Let x = the number of times a person goes to the bathroom on a daily basis. Complete the values of x from least to greatest and the corresponding values of p(x) in the probability distribution table. X p(x)
For a particular disease, the probability that a patient passes away within the xth year is given by the following table: x P(x) 0 0.039 1 0.034 2 0.337 3 0.291 4 0.25 5 0.023 6 0.026 This means that the probability that someone passes away within the first year is 0.039. The probability that they pass away after one year would be 0.034. What is the mean number of years someone survives? (round to two decimal places) What is the standard deviation for the number of years someone survives? (round to two decimal places) The Range Rule of Thumb for survival would be: years to years. (Round each to two decimal places.) In your own words, interpret what the Range Rule of Thumb tells us about this disease. (If you don't remember what the Range Rule of Thumb is, review the heading "Unusual Values" in the Learning Activities.)
In a survey of 100 randomly selected dentists, 24 dentists recommended Pearly brand over the other 5 toothpastes. Predict how many dentists out of 350 would recommend Pearly brand toothpaste. Paragraph B I U A/ V ▶ || O ... 11.
A humane society claims that less than 72% of households in a certain country own a pet. In a random sample of 800 households in that country, 560 say they own a pet. At x = 0.01, is there enough evidence to support the society's claim? Complete parts (a) through (c) below. (a) Identify the claim and state Ho and Ha Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. % of households in the country own a pet. B. More than % of households in the country own a pet. %. O C. The percentage households in the country that own a pet is not D. Less than 72 % of households in the country own a pet. Let p be the population proportion of successes, where a success is a household in the country that owns a pet. State Ho and H₂. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to two decimal places as needed.) C. Ho: P Ho: p≤ 0.72 Ha:p>…
H H T T T H T H H T TH T H T H TH TH TH T The probability of obtaining two heads and two tails (Type an integer or a fraction.)
Three components are randomly sampled, one at a time, from a large lot. As each component is selected, it is tested. If it passes the test, a success (S) occurs; if it fails the test, a failure (F) occurs. Assume that 82.0% of the components in the lot will succeed in passing the test. Let X represent the number of successes among the three sampled components. Find P(X= 3). (Round the final answer to three decimal places.)
A random sample of 200 female high school students in India showed that 110 are on Facebook. A separate random sample of 150 male high school students in India showed that 69 are on Facebook. Let P1 and P2 be the proportion of all female and male high school students in India, respectively, who are on Facebook. Which the following are the estimate of p(combined), pc, and the standard test statistics, z, of the difference in the population proportions? O (C) pc = 0.51, z=pc = 0.51, z=(0.55 -0.46)-51/(0.51)(0.49)200+(0.51) (0.49)150 O pc = 0.11, z-(0.11 -0.51)-0V(0.51)(0.49)200+(0.51)(0.49)150 %3D O ic - 0.51, z-(0.55 -0.46)-0V(0.51)(0.49)200+(0.51)(0.49)150 %3D O ộc = 0.51, z-(0.55-0.46)-0v(0.46)(0.54)200+(0.55)(0.45)150 O Dc = 0.51, z-(0.55 -0.46)-0v(0.55)(0.45)200+(0.46) 54)150 Next STE 165 W
1st Class 2nd Class 3rd Class Perished 117 163 526 Survived 187 112 186 Total 304 275 712 The table contains data on the survival numbers for passengers by known ticket class for the RMS Titanic when it sunk. Does this data suggest that ticket class and survivability were dependent using α = 0.01?
This was what WAS given please helpppp
Let X be the total amount saved in dollars at the cash register. The pdf of X is given by: Value of X 20 28 40 50 58 70 probability 0.36 0.21 0.24 0.1225 0.0175 0.03 .0175 0.0025 Before I make the purchase, you would place my chance of saving $20 at 24%. Suppose you approach me after I pay for my items and ask: "Did you save any money?" If I answer "no", then you know I didn't save $20 and thus the chance of saving $20 changes from the unconditional chance 24% to the conditional chance 0%. However, if I answer "yes" my chance of saving $20 would get higher. What would be the conditional chance of saving $20 if you knew I got a discount? Mathematically, we seek: P(X = 20|X > 0 ). Even though it looks weird, it is just a conditional probability. Find it. P(X = 20|X > 0) = P(X = 20 and X > 0) / P(X > 0) = Hint: P(X = 20 and X > 0) be read off the table by identifying possible values where the event (X = 20 and X > 0) is true, don't use the multiplication rule. Do not round, express your…

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