# Question

Let X and Y be random variables of the continuous type having the joint pdf f(x, y) = 8xy, 0 ≤ x ≤ y ≤ 1.

Draw a graph that illustrates the domain of this pdf.

(a) Find the marginal pdfs of X and Y.

(b) Compute μX, μY, σ2X, σ2Y, Cov(X, Y), and ρ.

(c) Determine the equation of the least squares regression line and draw it on your graph. Does the line make sense to you intuitively?

Draw a graph that illustrates the domain of this pdf.

(a) Find the marginal pdfs of X and Y.

(b) Compute μX, μY, σ2X, σ2Y, Cov(X, Y), and ρ.

(c) Determine the equation of the least squares regression line and draw it on your graph. Does the line make sense to you intuitively?

## Answer to relevant Questions

For the random variables defined in Example 4.4-3, calculate the correlation coefficient directly from the Definition Using Example 4.4-2, (a) Determine the variances of X and Y. (b) Find P(−X ≤ Y). Let X and Y have a bivariate normal distribution with parameters μX = 10, σ2x = 9, μY = 15, σY2 = 16, and ρ = 0. Find (a) P(13.6 < Y < 17.2). (b) E(Y | x). (c) Var(Y | x). (d) P(13.6 < Y < 17.2 | X = 9.1). When α and β are integers and 0 < p < 1, we Have Where n = α + β − 1. Verify this formula when α = 4 and β = 3. Let X1, X2, X3 be a random sample of size n = 3 from the exponential distribution with pdf f(x) = e−x, 0 < x < ∞. Find P(1 < min Xi) = P(1 < X1, 1 < X2, 1 < X3)Post your question

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