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- The median of the random variable X whose probability density function 3 =x² ,0 < x < 2 - - f(y) = }2 ,0. W. isLet X ~ Beta(2, 1). In other words, the density of X is f(x) = { 2х, 0 0.36).3. The probability density functions of two statistically independent random variables X and Y are fx(x) = }u(x - 1)e-lx-1)/2 fr(y) =u(y- 3)e-(s-3)/4 Find the probability density of the sum W =X+Y.
- don't copy from cheggThe deviation of the size of an item from the midpoint of the tolerance field of width 2d equals the sum of two random variables X and Y with probability densities f(x) = -√2/² exp{-2²2} and p(y): √/2 exp{-20²2). Determine the (conditional) probability density of the random variable X for the nondefective items if the distribution p(y) does not depend on the value assumed by X.c) Let Y₁, Y₂,..., Yn be a random sample whose probability density function is given by f(v:B)= 684 - fa 00 0, elsewhere 200 200 200 and suppose that n = 200, y = 20, y = 100, y = 250 and $ = 0.025. i=1 i) Derive the standard error of ß, se(B) = 0.0009, using MLE approach. ii) Find an approximate 95% Confidence interval for B.
- 1 Random variables X' and Y'have the joint density fx., (x, y) = 4, 0Consider the probability density function P. (x) = a e-b lxl where X is the random variable which assum es all the values from - ∞ to o. Find CDr ) 4.suppose that f(y) = { 3y^2, 0<=y<=1 0, otherwise a) verify that f(y) is a valid probability density function.b) Determine the expected value of Yc) Determine the variance of Yd) Find the cumulative distribution function of Ye) Determine the probability that Y does not exceed 1/2The density function, ху fy(x, y) = f(x) =9 0, 03. The probability density functions of two statistically independent random variables X and Y are fx(x) = }u(x - 1)e-lx-1)/2 fr(y) =u(y- 3)e-(s-3)/4 %3D Find the probability density of the sum W =X+Y.Let Y1, Y2,..., Y, denote a random sample from the density function given by 1 yª-'e=y/®, y> 0, f(y[a, 0) = elsewhere, where a > 0 is known. a Find the MLE Ô of 0. b Find the expected value and variance of ê. c. Is the MLE ô an unbiased estimator for 0?SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON