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- 2. Let X be a Chi-squared random variable with density function fx(x) = exp (-;), a x > 0. Suppose Y is independent of, and has the same distribution as, X. (a) Let Z = VX. Show that the density function of Z is given by Sale) = 2a exp (-) z > 0. Hence state the value of a.Suppose that Y1, . . . , Yn is a random sample from a population whose density function isSuppose X = 1/(1+Y), where 3 Y ~ fy(y) = 12 1+y y > 0, 0, otherwise. Identify the distribution of X by name and parameter values.
- Let Yi,..., Yn denote a random sample from the density function given by fy (ul0) = ry"-le-"10, for 0 > 0, y > 0. where r is a positive constant. Find the MLE of 0. Is the estimator an MVUE for 0?Let X be a random variable with uniform distribution on the interval [-2,2]. Let Y be defined as Y = X5. Calculate the pdf of Y.Consider the following density function 4z(9–z²) 81 0Let X and Y are two random variables with p.d.f as F(x,y) = 3x^2y+3xy^2,0 < x< 1,0 < y < 1. (i) Find conditional density of X given Y. (ii) Find the mean, mode and standard deviation of r.v Y. (iii) Correlation between X and Y. (iv) Check that X and Y are independent or not?Let X1,., X, denote a random sample from the probability density function f(r) = 0xº-1, 0 0. Show that X is a consistent estimator of .5) (almost 5.26) Let Y,., Y, be iid with pdf f(y|0) = Oy-2 where 0<0Let Y1 < Y2 < Y3 be the order statistics of a random sample of size 3 froma distribution having the pdf f(x) = 2x, 0 < x < 1, zero elsewhere. Show thatZ1 = Y1/Y2, Z2 = Y2/Y3, and Z3 = Y3 are mutually independent.Let Y1 0 , zero elsewhere. Find E(Y1)Ук. Suppose that Y₁. Y₂; Yn 15. 2 from Function random Sample a population with probability density f(y) = find the maximum BY 1-B B like hood ozy 21: B >0 Elsewhere Estimator of BSEE MORE QUESTIONSRecommended textbooks for youAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Calculus 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,