Let Y;. Yz. --.. Y, denote a random sample from the probability density function e , y20, 0, elsewhere. Show that Y1) = min(Y1, Y2, .... Y,) is sufficient for e. %3!
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- 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 .Suppose that Y1, . . . , Yn is a random sample from a population whose density function isLet 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.
- Suppose X is a random variable taking values in the interval [0,2] with probability density function f(x) = 1-x/2. What is the variance of X?10) Let f(x) by the probability density function of some continuous random variable. Explain why it must be true that f(x) dx =1.Let X = (X,X,,.., X „) be a random sample with size n taken from population has 2..., probability density function fx (x;0) = e®-*) ,x> 0. Prove that U = min(X)is a sufficient statistic for 0.
- Let Y₁, Y2,..., Y₁ denote a random sample from the probability density function f(y) = {0y⁰-1₁ 0 0. Show that Y is a consistent estimator of 0/(0+1).Let X be a random variable with pdf f(x) = kx*,-1Let X ~ U[0,1] and Y = -βln(1-X). What is the distribution of Y? Justify.If X ~ U(3, 15), what is the probability density function for this distribution?Let X1, X2, . X6 be an i.i.d. random sample where each X, is a continuous random variable with probability density function f(x) = e-(-0) , x > 0 Find the probability density function for X(6).Let the density function of a random variable X be given by fx(x) = 0x®-', 0SEE MORE QUESTIONSRecommended textbooks for youCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,