Let X ~Par (2) and Y = ln(X). Compute P(Y > 1).
A. 1 - dx x(ln x) (Hint: Let u = ln x) 2 B. v3 arctan x - dx 1+2 م 1/2 م ccosx dr [use cost on p.494 prob. 44 formula]
let u= ln(x) and v=ln(y) w=ln(z) where x,y,z>0 .Write thr following wxpressiins in terms of u,v, and w. a) ln( squareroot x^5)/ y^3z^2) B) ln (squareroot x^3 4squaroot y)
2. Let X and Y be independent integer-valued RVs with given distributions jezqj = 1. (a) Compute the probability P(X = IYI). (b) Compute the probability P(Y/X є Z).
2. Let X and Y be independent integer-valued RVs with given distributions jezqj = 1. (a) Compute the probability P(X = IYI). (b) Compute the probability P(Y/X є Z).
Let U ~uniform(0,1). Let Y =−ln(1−U). hint: If FX (x) = FY (y) and supports x,y ∈ D, X and Y have the same distribution. Find FY (y) and fY (y). Now, it should be straight forward that Y follows distribution with parameter_____________-
Let D = {(x, y) ∈ R^2 | x^2 + y^2 ≤ 1} and let p, q ∈ int(D) be
two distinct points. Prove that there exists a homeomorphism h : D
→ D interchanging p and q.Help!!
(x, y)E R22 y < 1} and let p, q E int(D) be two distinct points (8) Let D Prove that there exists a homeomorphism h : D -> D interchanging p and q.
(x, y)E R22 y D interchanging p and...
Please explain b!
2. Let z = f(x, y) = ln(4x2 + y2) (a) Use a linear approximation of the function z = f(x,y) at (0,1) to estimate f(0.1, 1.2) (b) Find a point P(a,b,c) on the graph of z = f(x, y) such that the tangent plane to the graph of z = f(x,y) at the point P is parallel to the plane 2x + 2y – 2=3
Let X ~ N(0,1), and let Y = 2X + 5. Compute P(Y <= 7)?
4) Suppose that Y~exp(8). Let X = ln(Y). Find the pdf of X. 5) Let Y and Y2 be iid U(0,1). Let S YY2. Find the pdf of S.
PROBLEM 1 Let the joint pdf of (X,Y) be f(x, y)= xe", 0<y<<< a. Compute P(X>Y). b. What is the conditional distribution of X given Y=y? Are X and Y independent? c. Find E(X|Y = y). d. Calculate cov(X,Y).
(1 point) Let x = 2 and y = 5 . Compute ||x – y||ı = ||X – yllco = ||X – yl|2 = Hue