9 Consider the probability distribution function f(x) = { 1 ≤ x ≤ 3 elsewhere Calculate the mean value of x and the probability that 0 ≤ x ≤ 2 20 0
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- 4. Let X be a continuous random variable with probability distribution +k 0≤x≤3 otherwise f(x) 0 Find k, and P(1 ≤X ≤ 2). 1The percentage of vehicles on a freeway that violate the speed limit is π = 0.88 You randomly clock n = 80 vehicles. 32) The probability that between 66 and 70 vehicles violate the speed limit is P(66 ≤ x ≤ 70) = a 0.4350 b 0.4438 c 0.4529 d 0.4621Let X represent a continuous random variable with a uniform distribution over the interval from 0 to 4. What is P(X < 0.9)?
- GjcvThe table shown below gives six pairs of x and y values. y 16 8 20 13 12 9. 10 4 9. 9 4 Using the regression of y on x, the predicted value of y for x = 17, rounded to two decimal places, is:The amount of time it takes Susan to wait for the bus is continuous and uniformly distributed between 4 minutes and 18minutes. What is the probability that it takes Susan less than 5 minutes given that it takes less than 11 minutes for her to wait for the bus
- Compute P(X) using the binomial probability formulaThen determine whether the normal distribution can be ed to estimate this probabilityIf soapproximate P(X) using the normal distribution and compare the result th the exact probability n=53, p = 0.7 and X = 41poisson distributionLet X have a uniform distribution on the interval (2, 9). Find the probability that the sum of 2 independent observations of X is greater than 16.
- Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded egion of the graph. Assume the variable x is normally distributed. Pregnancy Length in a Population of New Mothers H= 269 o = 10 283D5) X and Y are two points that are selected according to a uniform distribution. Calculate the expected value of the distance between these two points for each of the following cases: a) Both X and Y are selected independently from the range 0-1. b) We select X between 0 and 1 and then select Y between 0 and X. Note: For case b the distance is equal to |Y-X|Births are approximately Uniformly distributed among the 52 weeks of the year. They can be said to follow a uniform distribution from one to 53 (spread of 52 weeks). 1. а. What is the probability distribution for X? For parts b – g include functions and shaded graphs b. Find the probability that a person is born at the exact moment week 19 starts Find the P(2Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. FreemanMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman