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- A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.b) Suppose that the joint density function of random variables X₁ and X₂ is given by f(x₁, x₂)= = 0, 0< x₁ < x₂ <2 otherwise i) Draw a sketch of the area where f(x₁, x₂) is not zero. ii) Find P(X₂ < 1). iii) Find E(X₁X₂).3. Let X be a scalar random sample from the following density f(x) = 2(0-x) 82 Construct a (1-a) Cl for 0. for 0 ≤ x ≤ 0
- Determine k so thatf(x, y) = kx(x − y) for 0 < x < 1, −x < y < x0 elsewherecan serve as a joint probability density.For x1, the marginal distribution fx1 (x1) function is validis it a density function)2. The talk time (in hours) on a cell phone in a month is approximated by the probability density function: f(x) = = x-10 5h h 25-x 5h for 10 < x < 15 for 15 ≤ x ≤ 20 for 20 < x < 25 a) What is the value of the constant h? b) P(X < 17.5) = ? c) P(X<22.0) = ? d) What is the length of the shortest 95% of calls?
- The joint density of X and Y is given by, ху, Iw(x, y) = (x² +: 0 l) b) Find the marginal probability distributions of X and Y. c) Find the conditional probability density function of Y given X=0.5 and calculate P(YLet X1 and X2 be two continuous random variableshaving the joint probability density f(x1, x2) = 4x1x2 for 0 < x1 < 1, 0 < x2 < 10 elsewhereFind the joint probability density of Y1 = X21 and Y2 = X1X2.Let X be a continuous random variable with density function(x) = 4 1. Determine F(5) 2. Determine p(1Suppose that X and X, have joint probability density function x2, if 1< xı < 2 and 1 < r2 < 3 10, fx1.x.("1, 2) = otherwise. What is the joint probability density function fy,y, of Y1 = X1/X2 and Y, = X2?ASAPLet X₁, X2, X3, X30 be a random sample of size 30 from a population distributed with the following probability density function: f(x) = (0, -, if 0SEE MORE QUESTIONSRecommended textbooks for youCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Functions and Change: A Modeling Approach to Coll…AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Functions and Change: A Modeling Approach to Coll…AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning