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- Suppose div F = 0 in a region enclosed by two concentricspheres. What is the relationship between the outward fluxesacross the two spheres?Assume the proportion of the time within a year, Y, and any flood by Kucuk Menderes River is determined to approximately follow a beta density function below; fW) = { 50 5(1 – y)*, 0< y < 1, 0, elsewhere, a) Find a and B b) Without using any table or source, find the chance that the flood occurs at most 10% of a year?2. A printer ink cartridge has a life of X hours. The variable X is modeled by the probabil: S 400x-2 x > 400 density function f(x) = %3D otherwise Calculate a) median lifetime of these cartridges b) value of b such that P(X < b) = 0.6
- 2. If X and Y are continuous random variables having joint density function f(x,y) = {y^¹, if 03) The joint density of X and Y is f( x, y) = 2e**2) for x > 0, y > 0 and f( x, y) = 0 otherwise. a) Find the joint cumulative distribution function. b) Find P( XSuppose X,Y have joint density function f(x,y) = (12/7)(xy+y^2), 0 <= x <= 1 and 0 <= y <= 1 and 0, otherwise. a) Check that f is a genuine joint density function. b) Find the marginal density functions of X and Y. c) Calculate the probability P(X < Y).Recommended textbooks for youCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage