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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.Determine k so thatf(x, y) = kx(x − y) for 0 < x < 1, −x < y < x0 elsewherecan serve as a joint probability density.The life lengths of two transistors in an electronic circuit is a random vector (X; Y ) where X is the life length of transistor 1 and Y is the life length of transistor 2. The joint probability density function of (X; Y ) is given by | 2e-(x+2y) x 2 0, y 20 fx,y(x,y) = fx.MX.v) else Then the probability that the first transistor last for at least half hour given that the second one lasts at least half hour equals Select one: a. 0.3669 b. 0.3935 c. 0.7772 d. 0.6318 e. 0.606
- The probability density of the random variable Z isgiven by f(z) = kze−z2for z > 00 for z F 0Find k and draw the graph of this probability density.Let X and Y be two continuous random variables with joint probability density function f(x,y) = 2xy for 0 < x < y < 1. Find the covariance between X and Y.ASAP
- Let X and Y has joint probability density function * y? A(X, Y) 81 ,0Let X and Y be two continuous random variables with joint probability density function: 6e-(2x+3y)+k x21, y > 0 fxy (x, y) = otherwise a) Find the coefficient k. b) Find P(X 2). c) Find the marginal probability density functions of X and Y ( fx(x), f;(y)). d) Are X and Y independent?Let X and Y be two continuous random variables hav-ing the joint probability density f(x, y) = 24xy for 0 < x < 1, 0 < y < 1, x + y < 10 elsewhere Find the joint probability density of Z = X + Y andW = X.Let X be a continuous random variable with density function(x) = 4 1. Determine F(5) 2. Determine p(1fxlx,y) = x2y is a joint probability density function over the range 02. Let f(x, y) be the probability density function of the continuous random variable (X, Y). If U = XY, show that the probability density function of U is given by fu(u) = [ƒ€.) | dv. ( , v) |SEE 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