Let f(x,y) = (8/7)xy, 0 ≤y ≤x ≤2 (a) Draw a graph that represents the domain of this pdf. (b) Find P(Y ≤1) (c) Find the marginal pdfs fX(x) and fY(y) (d) Compute μX, μY, σ2X, σ2Y, Covariance (X,Y ), and ρ (e) Find the equation of the least squares regression line and draw it on your graph. Does the line make sense to you intuitively?
Let f(x,y) = (8/7)xy, 0 ≤y ≤x ≤2 (a) Draw a graph that represents the domain of this pdf. (b) Find P(Y ≤1) (c) Find the marginal pdfs fX(x) and fY(y) (d) Compute μX, μY, σ2X, σ2Y, Covariance (X,Y ), and ρ (e) Find the equation of the least squares regression line and draw it on your graph. Does the line make sense to you intuitively?
Let f(x,y) = (8/7)xy, 0 ≤y ≤x ≤2 (a) Draw a graph that represents the domain of this pdf. (b) Find P(Y ≤1) (c) Find the marginal pdfs fX(x) and fY(y) (d) Compute μX, μY, σ2X, σ2Y, Covariance (X,Y ), and ρ (e) Find the equation of the least squares regression line and draw it on your graph. Does the line make sense to you intuitively?
3. Let f(x,y) = (8/7)xy, 0 ≤y ≤x ≤2 (a) Draw a graph that represents the domain of this pdf. (b) Find P(Y ≤1) (c) Find the marginal pdfs fX(x) and fY(y) (d) Compute μX, μY, σ2X, σ2Y, Covariance (X,Y ), and ρ (e) Find the equation of the least squares regression line and draw it on your graph. Does the line make sense to you intuitively?
Definition Definition Measure of how two random variables change together. Covariance indicates the joint variability or the directional relationship between two variables. When two variables change in the same direction (i.e., if they either increase or decrease together), they have a positive covariance. When the change is in opposite directions (i.e., if one increases and the other decreases), the two variables have a a negative covariance.
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