Let (X,Y) be a two-dimensional random variable with the joint pdf {6xy 0
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- Let X,Y be i.i.d. random variables from U(0,1) distribution. (a) Give the joint distribution of X+Y and X-Y. Are they independent? Justify your answer. (b) Give the marginal distributions of X + Y and X - Y. (c) Compute E(X2 - Y).R3Consider the Weibull distribution with pdf fx (x) = 3x²e¬**, x > 0. Derive the Hazard rate function (failure rate) fx (t) R (t) : %3D 1- Fx (t)
- A random variable Y have a distribution with parameter a > 0 and yo > 0 if its density function is given by: ´ayf f(y) = {ya+1 (0, if y > yo elsewhere ii) ayg (a-2)(a-1)2" Show whether or not that the variance of Y is1 Random variables X' and Y'have the joint density fx., (x, y) = 4, 0Consider two continuous random variables X and Y with joint pdf f(x,y)= 24x for 0Page 263, 4.4.8We have a random variable X and Y that jave the joint pdf f(x) = {1 0<x<1, 0<y<1} {0 otherwise} Let U = Y - X2. What is the support for the random variable U? Are there critical points? If U = Y/X. What is the support for the random variable U? Are there critical points?Let X1,...,X, be independent random variables with pdfs -{* 0 -i(0 – 1) 0. Find a two-dimensional sufficient statistic for 0.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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