- A Bivariate Random Variable X Y Has Joint Probability Density Function Pdf F 3 9 8xy 0 X Y 1 0 Otherwis 1 (96.75 KiB) Viewed 26 times
A bivariate random variable (X,Y) has joint probability density function (pdf) f(3,9) = { 8xy, 0 < x < y < 1 0, otherwis
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A bivariate random variable (X,Y) has joint probability density function (pdf) f(3,9) = { 8xy, 0 < x < y < 1 0, otherwis
A bivariate random variable (X,Y) has joint probability density function (pdf) f(3,9) = { 8xy, 0 < x < y < 1 0, otherwise. (a) Find the marginal distributions of X and Y. Use this to determine whether X and Y are independent. (b) Find the conditional pdf of Y given that X 5. What is the value of the probability P(Y > Ž|X = 3)? (c) Let the random variables U and V be defined by 5 X U = Y V=Y. (i) Find the joint pdf of (U, V) and clearly specify the domain of U and V. (ii) Find the marginal pdf of U.