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Random variables
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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?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) = 0.62. If X and Y are continuous random variables having joint density function f(x,y) = {y^¹, if 0Assume 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?An electronic system has one each of two different types of components in joint oper- ation. Let Y₁ and Y₂ denote the random lengths of life, in hundreds of hours, of the components of type I and type II, respectively. The joint density function is given by: f(y₁, y2) = [(1/8)y₁e¯(v₁+y²)/²_if y₁ > 0, y2 > 0 elsewhere 0 (a) Verify that f(y₁, y2) is a probability density function. (b) Find P(Y₁ > 1, Y2₂ > 1). (c) Find the probability that a component of type II will have a life length in excess of 200 hours. (d) Is fy₁,Y₂ (y₁, y2) = fy₁ (₁) fy₂ (Y2)? (e) One way to measure the relative efficiency of the two components is to compute the ratio Y₂/Y₁. Find E(Y₂/Y₁).Suppose 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