2. For the function y=2(x - 2)/2, where I > 2, find and simplify (a) an...
If X and Y have a joint probability density function specified by 2-(+2y) find P(X <Y).
F. dr Find a function of such that of 8 and then evaluate where F(x, y) = < 3 + 2kg", 2y) and C is any smooth curve from (-2, 1) to (1,2).
#2. (24 points) Let X and Y have joint density (a) Find the marginal pdf of Y. Use it to find E(Y) (b) Give an integral expression for P(X + Y < 0.75), but do not evaluate. (c) Give an integral expression for E(XY), but do not evaluate. Optional two point bonus problem. In Problem 2 above, is the distribution of Y skewed to the left or skewed to the right? Explain. #1. (28 points) Suppose that X has probability...
17. Given f(x, y, z) = x^yz -- xyz', P(2,-1,1) and vector v =<1,0,1 >. Find i. the directional derivative of the function at the point P in the direction of v. ii. the maximum rate of change of f.
2.5.1. The probability function of a random variable Y is given by where λ is a known positive value and c is a constant. (a) Find c. (b) Find P(Y 0). (c) Find P(Y>2).
4. Let 3 f(x, y, z) = x’yz-xyz3, 4 P(2, -1, 1), u =< 0, > 5 a). Find the gradient of f. b). Evaluate the gradient at the point P. c). Find the rate of change of f at the point of P in the direction of the vector u.
function Ckek osrs4 be a density 4. Let f(x)=3 otherwise Find: i) k = 24] P(-2<x<2)
b. Simplify 81-17 y13 where I, Y > 0 rºy
4. The joint distribution of X and Y is given by 0 otherwise (a) Are X and Y independent? Explairn. (b) Find the marginal probability function (pdf) of Y, fy (). (c) Provide the integral for finding P(X < Y), but DO NOT evaluate.
7. Given the joint density function /(x,y) =(kx (1 + 3 y*) 0<x<2,0<p?1 elsewhere a. Find k, g() h) and f(x) b. Evaluate P(-<X<1)