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- if (xoy) - X 2 2 · 10-10 3 0.15 0.20 0.30 5 0·10 0·15 a. Determine the marginal distribution g(x), x=2, 4 b. Determine the marginal distribution h(y), y = 1,3,5 c. Determine the cumulative distribution punction F(x) 4STAT 202: Individual Assignment x>0 1. Given the Gamma distribution as f(x) =- elsewhere Find the mean and variance of the distribution. 2a. Suppose that a large conference room for a certain hotel can be reserved for no more than 4 hours. However, the use of the conference room is such that both long and short conferences occur quite often. In fact, it can be assumed that length X of a conference has a uniform distribution on the interval [0, 4]. i. Determine the probability density function ii. What is the probability that any given conference last at least 3 hours? b. A cement wholesale distributor has a large store that hold fixed supplies and are filled every Sunday. Of interest to the wholesaler is the proportion of this supply that is sold during the week. Over many weeks of observation, the distributor found out that this proportion could be modeled by a beta distribution with a = 4 and ß = 2 . Find the probability that the wholesaler will sell at least 90% of his stock in a…f(x, y) 1 0.05 0.05 0.00 g (x) 0.10 a. Determine the mean of X. b. Determine the mean of Y. y 1 3 5 X 2 0.05 0.10 0.20 0.35 3 0.10 0.35 0.10 0.55 h (y) 0.20 0.50 0.30 1
- Let X-T(4) and Y~ x2 (4). The following plot depicts the cumulative distribution functions of X and Y. We don't know which is which. The horizontal lines have values 25% and 75%. We denote by q1 the x-coordinate correponding to the red point and by q2 the x-coordinate corresponding to the blue point. Which of the following statements are true? 1.00 - 0.75 0.50 - 0.25+ 0.00 - The answer is : The cdf of X corresponds to the red curve while the one of Y corresponds to the blue curve. Can you explain why? Density11 Assume the GPAS of high school students, X, follows a continuous uniform on the domain 1just 1a)Why do we use the three intervals listed here? How do we pick the intervals to test?cumulative distribution function for heights (in meters) of trees in a forest is F(x). (a) Explain in terms of trees the meaning of the statement F (7) = 0.5. F (7) = 0.5 tells us that i (b) Which is greater, F (7) or F (6)? Justify your answer in terms of trees. because every tree of height eTextbook and Media % of the trees in the forest have Same for stor meters also has height mete(1.5,2) 1.5 (0,7, 0.2) f0.7,0.2) O5 ー15 -0.5 0.5 1.5 - 0.57 (-1.2,-1) - 15 -2 what are the values Inthe losed interval (-1.2,1.5) where 'undehned? What are the crithcal valuesof f? at x = %3D Where is f's0? xin theinterval Where is f'SEE MORE QUESTIONSRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,