et (X, Y)' be a random vector with the following density function: (8xy ifosasysl elsewhere ind the marginal density functions of X and Y. Are X and Y independent? f(x)=
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- Find the distribution function and density function of Y = sinX, where X is distributeduniformly between 0 and 2π.Please be specific.The random vector (X,Y) has the following joint probability density function:f(X,Y)(x,y) ={4xye−(x^2+y^2), x >0, y >0, 0, otherwise LetZ=√(X2+Y2) Find the probability density of the random variableZ.
- There are two components in an electronic system. Let X and Y denote the lengths of life in years. The joint density function of these variables f(x, y) = {ye-&+x) ,x 2 0, y Determine P(x>3) What is the probability that both components will exceed 3 years?Let X and Y be continuous random variables with joint density function f(x, y) =x?y, 0 < x < y < 1 %3D Otherwise. What is the joint density of U = and V = Y ? YX and Y re random losses with joint density funcTion 2C forocn<00 500000 An Insurance losses pays the total of the twX9 losses to a maximum and oey< lo0, 100 policy on the payment of 100 the expectic fpagment the insurer will make on this policy.
- Let A > 0. Suppose (X, Y) has joint probability density function given, for all x, y E R, by 3. fx,y(x, y) = { Ay exp(-y(x+ A)), if a 2 0 and y > 0 0, otherwise. (i) Calculate the marginal density of Y. (ii) Let y > 0. Find the the conditional probability density function of X given Y = y. Interpret your answer. (iii) Calculate E[X|Y] and prove that E[X] = +oo. Hint: You can use without a proof that -dy = +oo. %3DGiven the function fxy (x, y) = b (x+y)² for - 2Suppose that (X,Y)' has a density function given by for a > 1, y > 0, f(x, y) = 10, otherwise. Determine the distribution of X?Y.Now, assume that Y₁,..., Yn distributed iid, each with density -{* where is positive constant. Find the density function for fy) (y). fy(y) = e-(-0), 0, if y> 0; otherwise,A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X be the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is fo fkr², if 02. Consider the joint density function 16M f(x,y) = {#, z> 2,0SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON