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1. Consider the following distribution of (X Y) where X and Y ae both binary random...
1. Consider the following distribution of (X,Y) where X and Y are both binary random variables:...
1. Consider the following distribution of (X,Y) where X and Y are both binary random variables: 1/4 if (, y) (0,0) 1/8 if(x, y) = (1,0) 3/8 if (, y) (0,1) y(2, y) = 1/4 if(x, y) = (1,1). (f) What is the covariance between Y and Xi
1. Consider the following distribution of (X,Y) where X and Y are both binary random variables:...
1. Consider the following distribution of (X,Y) where X and Y are both binary random variables: JA if (z, y) = (0,0) 1/8 3/8 if(x, y) = (1,0) if (x, y) = (0, 1) y(2, y) = 1/4 if(x, y) = (1,1). () What is the covariance between Y and X?
1. Assume that X and Y are both binary random variables. Assume that there are constants,...
1. Assume that X and Y are both binary random variables. Assume that there are constants, Bo and B such that Y-Ao + AX + t. Assume Elu 1 X-0. (a) Express EY | X-0nters of Bo and B1. (b) Express EY | X = 1] in terms of A, and A. (c)Assume that the joint pdf for (X, Y) is 1/4 f(,y) (0,0) 1/8 if(x, y) = (1,0) 3/8 if (r, y) (0,1) 1/4 if (x,y) - (1, 1)....
1. Let X and Y be two discrete random variables each with the same the possible...
1. Let X and Y be two discrete random variables each with the same the possible outcomes {1,2,3} a) Construct a bivariate probability mass function Px.y : {1,2,3} x {1,2,3} + R that satisfies the following properties propeties: (i) The expectation of X is E[X] = 2.1, (ii) The conditional expectation of Y given 2 = 3 is EY 2 = 3] = 1, (iii) The correlation between X and Y is slightly positive so that 0 < corr(X,Y) <...
Exercises: 1) The joint distribution of X and Y is given by the following table: y...
Exercises: 1) The joint distribution of X and Y is given by the following table: y 1.5 2 fxy(x, y) 1/4 1/8 1/4 1/4 1/8 Compute: a) P(X=1.5, Y =2). b) P(X=1, Y =2). c) P(X=1.5). d) P(X<2.5, Y<3) e) P(Y>3) f) E(X), E(Y), V(X) and V(Y). g) The marginal distributions of X and of Y. h) Conditional probability distribution of Y given that X = 1.5. i) E(Y|X=1.5) j) E(XY) k) Are X and Y independent? Explain why or...
Let X and Y be a random variable with joint PDF: f X Y ( x...
Let X and Y be a
random variable with joint PDF:
f X Y ( x , y ) = { a
y x 2 , x ≥ 1 , 0 ≤ y ≤ 1 0 otherwise
What is a?
What is the conditional PDF of given ?
What is the conditional expectation of given ?
What is the expected value of ?
Let X and Y be a random variable with joint PDF: fxv (, y) = {&, «...
Suppose X and Y have joint distribution function given by: p(x, y) = for (x, y)...
Suppose X and Y have joint distribution function given by: p(x, y) = for (x, y) = (-1,0), (0,1), (1,0). (a) Are X and Y independent? (b) Find the Covariance of X and Y.
Consider a continuous random vector (Y, X) with joint probability density function F(x,y) = e-y for...
Consider a continuous random vector (Y, X) with joint probability density function F(x,y) = e-y for 0<x<y<∞ Compute the marginal density of X denoted by f(x). Compute the conditional density of Y given X denoted by f(y|x). Hint: Consider the two cases y > x and y ≤ x separately. Compute the conditional expectation E[Y |X = x]. Compute the conditional variance Var(Y |X = x).
you have two random variables, X and Y with joint distribution given by the following table:...
you have two random variables, X and Y with joint distribution given by the following table: Y=0 | .4 .2 4+.26. So, for example, the probability that Y 0, X - 0 is 4, and the probability that Y (a) Find the marginal distributions (pmfs) of X and Y, denoted f(x),f(r). (b) Find the conditional distribution (pmf) of Y give X, denoted f(Y|X). (c) Find the expected values of X and Y, E(X), E(Y). (d) Find the variances of X...
Two random variables, X and Y, have joint probability density function f ( x , y...
Two random variables, X and Y, have joint probability density function f ( x , y ) = { c , x < y < x + 1 , 0 < x < 1 0 , o t h e r w i s e Find c value. What's the conditional p.d.f of Y given X = x, i.e., f Y ∣ X = x ( y ) ? Don't forget the support of Y. Find the conditional expectation E [...
1. Consider the following distribution of (X,Y) where X and Y are both binary random variables: 1/4 if (, y) (0,0) 1/8 if(x, y) = (1,0) 3/8 if (, y) (0,1) y(2, y) = 1/4 if(x, y) = (1,1). (f) What is the covariance between Y and Xi
1. Consider the following distribution of (X,Y) where X and Y are both binary random variables: JA if (z, y) = (0,0) 1/8 3/8 if(x, y) = (1,0) if (x, y) = (0, 1) y(2, y) = 1/4 if(x, y) = (1,1). () What is the covariance between Y and X?
1. Assume that X and Y are both binary random variables. Assume that there are constants, Bo and B such that Y-Ao + AX + t. Assume Elu 1 X-0. (a) Express EY | X-0nters of Bo and B1. (b) Express EY | X = 1] in terms of A, and A. (c)Assume that the joint pdf for (X, Y) is 1/4 f(,y) (0,0) 1/8 if(x, y) = (1,0) 3/8 if (r, y) (0,1) 1/4 if (x,y) - (1, 1)....
1. Let X and Y be two discrete random variables each with the same the possible outcomes {1,2,3} a) Construct a bivariate probability mass function Px.y : {1,2,3} x {1,2,3} + R that satisfies the following properties propeties: (i) The expectation of X is E[X] = 2.1, (ii) The conditional expectation of Y given 2 = 3 is EY 2 = 3] = 1, (iii) The correlation between X and Y is slightly positive so that 0 < corr(X,Y) <...
Exercises: 1) The joint distribution of X and Y is given by the following table: y 1.5 2 fxy(x, y) 1/4 1/8 1/4 1/4 1/8 Compute: a) P(X=1.5, Y =2). b) P(X=1, Y =2). c) P(X=1.5). d) P(X<2.5, Y<3) e) P(Y>3) f) E(X), E(Y), V(X) and V(Y). g) The marginal distributions of X and of Y. h) Conditional probability distribution of Y given that X = 1.5. i) E(Y|X=1.5) j) E(XY) k) Are X and Y independent? Explain why or...
Let X and Y be a
random variable with joint PDF:
f X Y ( x , y ) = { a
y x 2 , x ≥ 1 , 0 ≤ y ≤ 1 0 otherwise
What is a?
What is the conditional PDF of given ?
What is the conditional expectation of given ?
What is the expected value of ?
Let X and Y be a random variable with joint PDF: fxv (, y) = {&, «...
Suppose X and Y have joint distribution function given by: p(x, y) = for (x, y) = (-1,0), (0,1), (1,0). (a) Are X and Y independent? (b) Find the Covariance of X and Y.
you have two random variables, X and Y with joint distribution given by the following table: Y=0 | .4 .2 4+.26. So, for example, the probability that Y 0, X - 0 is 4, and the probability that Y (a) Find the marginal distributions (pmfs) of X and Y, denoted f(x),f(r). (b) Find the conditional distribution (pmf) of Y give X, denoted f(Y|X). (c) Find the expected values of X and Y, E(X), E(Y). (d) Find the variances of X...
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