Determine the conditional probability distribution of Y given that X = 1. Where the joint probability density function is given by f(x,y)=1/64xy for 0 < x < 4 and 0 < y < 4.
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- 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) = K(x2 + y2) 19 ≤ x ≤ 29, 19 ≤ y ≤ 29 0 otherwise (a) Determine the conditional pdf of Y given that X = x. fY|X(y|x) = for 19 ≤ y ≤ 29 Determine the conditional pdf of X given that Y = y. fX|Y(x|y) = for 19 ≤ x ≤ 29 (b) If the pressure in the right tire is found to be 22 psi, what is the probability that the left tire has a pressure of at least 25 psi? (It is known that K = 3 350,600 . Round your answer to three decimal places.) Compare this to P(Y ≥ 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 = 3 350,600…X is an exponential random variable with λ =1 and Y is a uniform random variable defined on (0, 2). If X and Y are independent, find the PDF of Z = X-Y2Suppose that that the RV X has the Gamma(2,β ) distribution for some β > = 0, E(X) = 2β and V (X) = 2β. Further, suppose that given X = x , the RV Y has the Unif (0, x) distribution. a) Write down the conditional pdf of Y given X = x (f_Y|X )(y | x) = b) Find the joint pdf of (X,Y) (f_XY)(x,y)= c) Find the conditional mean and variance of Y E(Y | X=x) =____________ V(Y |X=x )= ____________ d) Find the unconditional mean and variance of Y E( Y)= ____________ V(Y ) =____________ e) Find the marginal pdf of Y (f_y)( y)= ___________ f) Identify the distribution of Y Y-_________ g) Use parts e)- f) to find mean and variance of Y E(Y )=____________ V( Y)= ___________ The answer for Is 1/x (0<y<x) Β2 x/2 , (x2)/2 β , β please solve e) and f) and g)