# Question: Find k if the joint probability density of X Y

Find k if the joint probability density of X, Y, and Z is given by

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With reference to Exercise 3.65, find P(X + Y < 1/2 ). In exercise Find k if the joint probability density of X, Y, and Z is given by Check whether X and Y are independent if their joint probability distribution is given by (a) f (x, y) = 1/4 for x = - 1 and y = - 1, x = - 1 and y = 1, x = 1 and y = - 1, and x = 1 and y = 1; (b) f (x, y) = 1/3 for x = 0 ...If F(x1, x2, x3) is the value of the joint distribution function of X1, X2, and X3 at (x1, x2, x3), show that the joint marginal distribution function of X1 and X3 is given by M(x1, x3) = F(x1, ∞, x3) for - ∞ < x1 < ...The actual amount of coffee (in grams) in a 230- gram jar filled by a certain machine is a random variable whose probability density is given by Find the probabilities that a 230- gram jar filled by this machine will contain ...(a) If the probability density of X is given by Find E(X), E(X2), and E(X3). (b) Use the results of part (a) to determine E( X3 + 2X2 - 3X + 1).Post your question