The guess 0 was marked as incorrect.
E(Y|X=1)=1*(3/4)+(-1)*(1/4)=1/2
E(Y|X=-1)=(-1)*(3/4)+(1)*(1/2)=-1/2
E(Y)=E(Y|X=1)*P(X=1)+E(Y|X=-1)*P(X=-1)=(1/2)*(1/2)+(-1/2)*(1/2)=0
E(X)=xP(x)=1*(1/2)+(-1)*(1/2)=0
E(XY)=xyP(x,y)=1*1*(1/2)*(3/4)+1*(-1)*(1/2)*(1/4)+(-1)*(-1)*(1/2)*(3/4)+(-1)*(1)*(1/2)*(1/4)=0.5
therefore Cov(X,Y)=E(XY)-E(X)*E(Y)=0.5-0*0 =0.5
The guess 0 was marked as incorrect. Suppose we have a random variable X such that...
Suppose we have a random variable X such that X-1 with probability 1/2 and X =-1 with probability 1/2·We also have another random variable Y such that Y-X with probability 3/4 and YX with probability 1/4. What is the covariance between them, Cov(X, Y)?
1. Suppose we have three random variables Y1 , Y2 , and Y3 .
Suppose we have three random variables Y, Y,, and Y,. The standard deviations of Y and Y, are both 3 and the standard deviation of Y is 2. The correlation coefficient between Y and Y, is-0.6. The covariance between Y and Y, is 0.5. Y is independent of Y 1. 1 2 a) (3 pts) Find Var(h + 3%) b) (3 pts) Find Cov(3h + 2⅓'5½-%)
Let the random variable X and Y
have the joint probability density function.
fxy(x,y) lo, 3. Let the random variables X and Y have the joint probability density function fxy(x, y) = 0<y<1, 0<x<y otherwise (a) Compute the joint expectation E(XY). (b) Compute the marginal expectations E(X) and E(Y). (c) Compute the covariance Cov(X,Y).
between 0 and 4, x-UlO,4]. Another random variable, Y, is given Q1) Random variable as a function of g(x), Y X has uniform distribution g(x) where g(x)- 3-х, 2 x < 3. 0, otherwise. For parts a, b, and c, plotting the function y g(x) can be very useful. a-What is P(Y 0) [4 points] b-What is P(Y 1) 13 points] c-Derive and plot the cumulative distribution function (CDF) of Y, Frv). [10 points) d-What is probability distribution of Y,...
between 0 and 4, x-UlO,4]. Another random variable, Y, is given Q1) Random variable as a function of g(x), Y X has uniform distribution g(x) where g(x)- 3-х, 2 x < 3. 0, otherwise. For parts a, b, and c, plotting the function y g(x) can be very useful. a-What is P(Y 0) [4 points] b-What is P(Y 1) 13 points] c-Derive and plot the cumulative distribution function (CDF) of Y, Frv). [10 points) d-What is probability distribution of Y,...
3. Let the random variables X and Y have the joint probability density function 0 y 1, 0 x < y fxy(x, y)y otherwise (a) Compute the joint expectation E(XY) (b) Compute the marginal expectations E(X) and E (Y) (c) Compute the covariance Cov(X, Y)
3. Suppose we have a random variable X with mean a new random variable Y as = 7 and variance a4. We define Y 3 5X Find the standard deviation of Y
Suppose the random variables X, Y and Z are related through the
model
Y = 2 + 2X + Z,
where Z has mean 0 and variance σ2 Z = 16 and X has variance σ2
X = 9. Assume X and Z are independent, the find the covariance of X
and Y and that of Y and Z. Hint: write Cov(X, Y ) = Cov(X, 2+2X+Z)
and use the propositions of covariance from slides of Chapter
4.
Suppose the...
3. Let the random variables X and Y have the joint probability density function fxr (x, y) = 0 <y<1, 0<xsy otherwise (a) Compute the joint expectation E(XY). (b) Compute the marginal expectations E(X) and E(Y). (c) Compute the covariance Cov(X,Y).
1 3 4 9. Suppose the discrete random variables X and Y are jointly distributed according to the following table: Yl-1 0 1 0.1 0.1 0.1 0 0.2 0.1 0.2 0.1 0.1 a. Compute the expected values E(X) and E(Y), variances V(X) and V(Y), and covariance Cov(X,Y) of X and Y. (11) b. Let W = X - Y. Compute E(W) and V(W). [4] 10. Let X be a continuous random variable with probability density function h(x) ce* r >...