HW7 - Stat4714HW7:Chapter5JointDistributions...

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Due Monday October 11 at 2:30pm (1) Let Y1 and Y2 be discrete random variables with a joint probability distribution as shown in the table  below.    (a) Verify that this is a valid discrete joint probability  distribution. (b) Find the marginal distribution of Y1. (c) Find the marginal distribution of Y2. (d) Show that Y1 and Y2 are dependent but have a zero covariance. (2) Given the following function for X and Y, f(x,y) = c(x+y), (a) Find the value of c that makes this a continuous joint probability density function over the range  0<x<2 and x<y<x+2. (b) Determine P(X<1, Y<2). (c) Find covariance of X and Y. (d) Find correlation of X and Y. (e) Find the conditional density for Y given X. (f) Find P(Y>2|X=1). (3) Given the following function for x and y, f(x, y) = xy, 0 < x <1, 0 < y < 2,  (a) Find the marginal distributions for X and Y. (b) Determine if X and Y are independent variables.
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HW7 - Stat4714HW7:Chapter5JointDistributions...

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