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Suppose X andY are two dimensional random variables having joint p.d.f f(x,y) = find the p.d.f of u = Calculate Karl Pearson’s coefficient of correlation between X and Y X: 65 66 67 67 68 69 70 72 Y: 67 68 65 68 72 72 69 72 Given the joint pdf of X & Y. f X ,Y x, y CX ( x y );0 x 2; x y x 0 otherwise 1)Evaluate C 2)Find marginal pdf of X. 3)Find the conditional density of Y/X. Show that random process X(t) = A cos(t+) is wide sense stationary if a and are constants and is uniformly distributed random variable in ( 0,2).. If X(t)= A cosλt + B sinλt , where A and B are two independent normal random variables with E(A) = E(B) = 0 ,𝐸(𝐴2 ) = 𝐸(𝐵2 ) = 𝜎 2 , And λ is a constant , prove that {𝑋(𝑡)} is a strict sense stationary process of order 2. (at ) n 1 , n 1,2,... n 1 ( 1 at ) The process PX (t ) n at ,n 0 1 at (8) Show that X (t) is stationary or not. There are 2 white marbles in Urn A and 3 red marbles in Urn B.At each step of the process ,a marble is selected from each urn and the 2 marbles selected are interchanged. The state of the related Markov chain is the number of red marbles in urn A after the interchange .What is the probability that there are 2 red marbles in Urn A after 3 steps? In long run ,what is the probability that there are 2 red marbles inUrn A ? The equations of two regression lines are 3x+12y = 19 and 3y+ 9x =46. Find the correlation coefficient between X and Y. Define Wide sense stationary process. Give an example of evolutionary random process .