# Question: Let X and Y have the joint pdf f x y

Let X and Y have the joint pdf f(x, y) = x + y, 0 ≤ x ≤ 1, 0 ≤ y ≤ 1.

(a) Find the marginal pdfs fX(x) and fY(y) and show that f(x, y) ≠ fX(x)fY(y). Thus, X and Y are dependent.

(b) Compute

(i) μX,

(ii) μY,

(iii) σ2X, and

(iv) σ2Y.

(a) Find the marginal pdfs fX(x) and fY(y) and show that f(x, y) ≠ fX(x)fY(y). Thus, X and Y are dependent.

(b) Compute

(i) μX,

(ii) μY,

(iii) σ2X, and

(iv) σ2Y.

**View Solution:**## Answer to relevant Questions

Let X have a uniform distribution on the interval (0,1). Given that X = x, let Y have a uniform distribution on the interval (0, x + 1). (a) Find the joint pdf of X and Y. Sketch the region where f(x, y) > 0. (b) Find E(Y | ...Let Show that f(x, y) is a joint pdf and the two marginal pdfs are each normal. Note that X and Y can each be normal, but their joint pdf is not bivariate normal. Let X be N(0, 1). Find the pdf of Y = |X|, a distribution that is often called the half-normal. Hint: Here y ∈ S y = {y : 0 < y < ∞}. Consider the two transformations x1 = −y, −∞ < x1 < 0, and x2 = y, 0 < y < ∞. Let W have an F distribution with parameters r1 and r2. Show that Z = 1/[1 + (r1/r2)W] has a beta distribution. The lifetime in months of a certain part has a gamma distribution with α = θ = 2. A company buys three such parts and uses one until it fails, replacing it with a second part. When the latter fails, it is replaced by the ...Post your question