If < x >=< y > how are x and y related
Suppose random variables X and Y are related as Y=7X+3. Suppose the random variable X has mean 1, and variance 1. What is the expected value of X+Y ? Solution provided is 11. How was this obtained?
Assume that x and y are functions of t, and x and y are related by the equation y= 4x+3. (a) Given that dx/dt=1, find dy/dt when x=2. (b) Given that dy/dt=4, find dx/dt when x=3.
If x and y are positively related, what is the coefficient of correlation when r2 = 23.4%? ________________. If x and y are inversely related, what is the coefficient of correlation when r2 = 77.7%? ________________.
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...
How are these graphs related
a) reflected about y=0
b) reflected about y=x
c) reflected about y=-x
d) all identical
π-2 π-2 π-2 π-2 π-4 π-4 π-4 π-2 π-2 π-2 π-2 π-4 π-4
π-2 π-2 π-2 π-2 π-4 π-4 π-4 π-2 π-2 π-2 π-2 π-4 π-4
4. The rv y is linearly related to the rv X: Y = aX+b. Find the variance of yin terms of the mean and/or variance of X.
The variables x and y are implicitly related to the equation x^4+ { ^Y down 1 e^-t^2 dt =1 ( Y is at the top of the { and 1 is at the bottom of the { ) The point p=(1,1) lies on the graph of the equation. Find the slope of the line tangent to the graph at the point p=(1,1) A.) 2e^-2 B.) 2e C.) -4e D.) -4e^-1 E.) 4e^-2
P 1.3 A device has the output, y, and input, x, which are related by y = 2x + x Obtain a linearized model (a) When the operating point is x=1. (b) When the operating point is x = 2.
5. Suppose the random variables X, Y and Z are related through the model Y = 2 + 2X + Z, where Z has mean 0 and variance o2 = 16 and X has variance of = 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
5. Suppose the random variables X, Y and Z are related through the model Y = 2 + 2X + 2, where Z has mean 0 and variance o2 = 16 and X has variance of = 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