Two random variables X and Y with a joint PDF f(x,y) = Cx+y for 0≤ x ≤5 , 0≤ x ≤8 and constant C Find value of constant C

Let X, Y be independent random variables with exponential distribution of parameter θ > 0. Are the random variables Z = X + Y and W = X / (X+Y) independent?

Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable-X for the right tire and Y for the left tire, with joint pdf f(x, y) ĮK(x? + y?) 21 25). (Round your answer to three decimal places.) P(Y > 25) = (c) If the pressure in the right tire is found to be 22 psi, what is the expected pressure in the left tire, and what is the standard deviation of pressure in this tire? (It is known that K = Round your answers to two decimal 410,600 places.) expected pressure psi standard deviation psi